978-0134663890 Chapter 12 Part 3

subject Type Homework Help
subject Pages 14
subject Words 1257
subject Textbook Essentials of Chemical Reaction Engineering 2nd Edition
subject Authors H. Scott Fogler
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page-pf1
12-41$
P12-7)(c))continued$
$
$
Next$increase$the$coolant$flow$rate$and$run$the$same$program$to$compare$results.$
$
P12-7)(d)$
For$counter-current$flow,$swap$(T$–$Ta)$with$(Ta-T)$in$dTa/dV$equation$in$the$previous$Polymath$
See$Polymath$program$P12-7-d.pol.$
Calculated)values)of)the)DEQ)variables$
Variable$
initial$value$
minimal$value$
maximal$value$
final$value$
V$
0$
0$
10$
10$
X$
0$
0$
0.3647241$
0.3647241$
T$
300$
300$
463.44558$
450.37724$
Ta$
440.71$
440.71$
457.98124$
450.00189$
k$
0.01$
0.01$
3.7132516$
2.7077022$
Kc$
286.49665$
8.2274817$
286.49665$
9.9439517$
Fa0$
0.2$
0.2$
0.2$
0.2$
Ca0$
0.1$
0.1$
0.1$
0.1$
ra$
-1.0E-04$
-0.0256436$
-1.0E-04$
-9.963E-04$
Xe$
0.8298116$
0.3488462$
0.8298116$
0.381006$
DH$
-6000$
-6000$
-6000$
-6000$
Ua$
20$
20$
20$
20$
Fao$
0.2$
0.2$
0.2$
0.2$
sumcp$
30$
30$
30$
30$
mc$
50$
50$
50$
50$
Cpc$
1$
1$
1$
1$
page-pf2
12-42$
P12-7)(d))continued$
ODE)Report)(RKF45)$
Differential$equations$as$entered$by$the$user$
$[1]$d(X)/d(V)$=$-ra$/$Fa0$
$[2]$d(T)/d(V)$=$(Ua*(Ta-T)+(ra)*DH)/(Fao*sumcp)$
$
$
page-pf3
12-43$
P12-7)(e))Adiabatic)$
See$Polymath$program$P12-7-e.pol.$
Calculated)values)of)DEQ)variables$$
Variable$
Initial$value$
Minimal$value$
Maximal$value$
Final$value$
Ca0$$
0.1$$
0.1$$
0.1$$
0.1$$
Cpc$$
1.$$
1.$$
1.$$
1.$$
DH$$
-6000.$$
-6000.$$
-6000.$$
-6000.$$
Fa0$$
0.2$$
0.2$$
0.2$$
0.2$$
k$$
0.01$$
0.01$$
0.010587$$
0.010587$$
Kc$$
286.4967$$
276.8576$$
286.4967$$
276.8576$$
mc$$
50.$$
50.$$
50.$$
50.$$
Qg$$
0.6$$
0.6$$
0.6286162$$
0.6286162$$
Qr$$
0$$
0$$
0$$
0$$
ra$$
-0.0001$$
-0.0001048$$
-0.0001$$
-0.0001048$$
sumCp$$
30.$$
30.$$
30.$$
30.$$
T$$
300.$$
300.$$
301.0235$$
301.0235$$
Ta$$
450.$$
450.$$
450.$$
450.$$
Ua$$
0$$
0$$
0$$
0$$
V$$
0$$
0$$
10.$$
10.$$
X$$
0$$
0$$
0.0051176$$
0.0051176$$
Xe$$
0.8298116$$
0.827152$$
0.8298116$$
0.827152$$
$
2$$
d(T)/d(V)$=$(Ua*(Ta-T)+(ra)*DH)/(Fa0*sumCp)$$
3$$
d(Ta)/d(V)$=$Ua*(T-Ta)/mc/Cpc$$
$
Explicit)equations$$
1$$
Kc$=$10*exp(-6000/1.987*(1/450-1/T))$$
2$$
k$=$0.01*exp((10000/1.987)*(1/300-1/T))$$
3$$
Fa0$=$0.2$$
4$$
Ca0$=$0.1$$
5$$
ra$=$-k*(Ca0^2)*((1-X)^2-X/Ca0/Kc)$$
6$$
Xe$=$(2+1/Kc/Ca0-((2+1/Kc/Ca0)^2-4)^0.5)/2$$
7$$
DH$=$-6000$$
8$$
Ua$=$20*0$$
9$$
sumCp$=$30$$
10$$
mc$=$50$$
11$$
Cpc$=$1$$
12$$
Qg$=$ra*DH$$
13$$
Qr$=$Ua*(T-Ta)$$
page-pf4
12-44$
P12-7)(e))continued$
)
page-pf5
12-45$
P12-7)(e))continued$
$
$$
P12-7)(f))$
$
We$see$that$it$is$better$to$use$a$counter-current$coolant$flow$as$in$this$case$we$achieve$the$maximum$
P12-7)(g))$
)$
page-pf6
12-46$
P12-7)(g))continued$
$
$
$
P12-8$
Refer)to)solution)P11-6$
Heat)Exchange$ $ $
$ $ $ $ $
$
page-pf7
12-47$
P12-8)(a))Variable)Ta)Co-Current$
$
page-pf8
12-48$
P12-8)(b))Gas)Phase)Counter)Current)Heat)Exchange)Vf))=)20)dm3$
$
Note:$y$=$P$=$
P
P
$in$5th$Edition$$
$
page-pf9
12-49$
P12-8)(c)))Constant)Ta$
$
$
$
P12-8)(d))Refer$to$problem$P11-7$
$
P12-8)(e))Individualized$solution$
$
P12-8)(f))Refer$to$problem$P11-7$
$
$
page-pfa
P12-9$
Refer$to$solution$P11-7$$
)For)Heat)Exchanger
$ A$ terms$$$$$$$$$$$$1$→$15$$$$$$$$$$$$Same$as$adiabatic$
Energy$Balance$(20),$ $$
$(21)$ $
A$ Constant$Ta$(22A)$ Ta$=$300$K$
B$ Co-Current$Exchange$(22B)$
dT
a
Ua
ρb
"
#
$
$
%
&
'
'T−T
a
( )
$
page-pfb
12-51$
P12-9)(b))Counter)Current)Ta$
$
$
$
$
$
Gas$Phase$Counter$Current$Variable$Ta$
$
page-pfc
12-52$
P12-9)(b))continued$
Gas$Phase$Counter$Current$Variable$Ta$
$
Gas$Phase$Counter$Current$Variable$Ta$
$
page-pfd
12-53$
P12-9)(c))Constant)Ta$
$
$
$
$
$
$
$
Gas$Phase$Constant$Ta$
$
page-pfe
12-54$
P12-9)(c))continued$
Gas$Phase$Constant$Ta$
$
$
P12-9)(d))Refer)to)solution)P11-8)for)comparison)
$
$
P12-10)(a)$
For$reversible$reaction,$the$rate$law$becomes$
page-pff
12-55$
P12-10)(a))continued$
Polymath)Results$
Calculated)values)of)the)DEQ)variables$
Variable$
initial$value$
minimal$value$
maximal$value$
final$value$
$V$
0$
0$
10$
10$
$X$
0$
0$
0.0051176$
0.0051176$
$T$
300$
300$
301.02352$
301.02352$
$k$
0.01$
0.01$
0.010587$
0.010587$
$Fa0$
0.2$
0.2$
0.2$
0.2$
$Ca0$
0.1$
0.1$
0.1$
0.1$
$Kc$
286.49665$
276.85758$
286.49665$
276.85758$
$ra$
-1.0E-04$
-1.048E-04$
-1.0E-04$
-1.048E-04$
$Xe$
0.8298116$
0.827152$
0.8298116$
0.827152$
$
ODE)Report)(RKF45)$
Differential$equations$as$entered$by$the$user$
$[1]$d(X)/d(V)$=$-ra$/$Fa0$
$
$Explicit$equations$as$entered$by$the$user$
$[1]$T$=$300+200*X$
$[2]$k$=$.01$*$exp((10000$/$1.987)$*$(1$/$300$-$1$/$T))$
$[3]$Fa0$=$0.2$
$[4]$Ca0$=$0.1$
$[5]$Kc$=$10$*$exp(-6000$/1.987$*$(1$/$450$-$1$/$T))$
$[6]$ra$=$-k$*$(Ca0$^$2)$*$((1$-$X)$^$2$-$X$/Ca0/$Kc)$
$[7]$Xe$=$(2+1/Kc/Ca0-((2+1/Kc/Ca0)^2-4)^0.5)/2$
$
$
$
$
page-pf10
12-56$
P12-10)(b)$
When$heat$exchanger$is$added,$the$energy$balance$can$be$written$as$
$
$
Where$Ua$=$20$cal/m3/s/K,$Ta$=$$450$K$
$
See$Polymath$program$P12-10-b.pol.$
$
Calculated)values)of)the)DEQ)variables$
Variable$
initial$value$
minimal$value$
maximal$value$
final$value$
$V$
0$
0$
10$
10$
$X$
0$
0$
0.3634806$
0.3634806$
$T$
300$
300$
455.47973$
450.35437$
$k$
0.01$
0.01$
3.068312$
2.7061663$
$Kc$
286.49665$
9.2252861$
286.49665$
9.9473377$
$Fa0$
0.2$
0.2$
0.2$
0.2$
$Ca0$
0.1$
0.1$
0.1$
0.1$
$ra$
-1.0E-04$
-0.0221893$
-1.0E-04$
-0.0010758$
$Xe$
0.8298116$
0.3682217$
0.8298116$
0.3810642$
$DH$
-6000$
-6000$
-6000$
-6000$
$Ua$
20$
20$
20$
20$
$Ta$
450$
450$
450$
450$
$Fao$
0.2$
0.2$
0.2$
0.2$
$sumcp$
30$
30$
30$
30$
)
ODE)Report)(RKF45)$
Differential$equations$as$entered$by$the$user$
$[1]$d(X)/d(V)$=$-ra$/$Fa0$
$[2]$d(T)/d(V)$=$((ra*DH)-Ua*(T-Ta))/(Fao*sumcp)$
$
$Explicit$equations$as$entered$by$the$user$
$[1]$k$=$.01$*$exp((10000$/$1.987)$*$(1$/$300$-$1$/$T))$
$[2]$Kc$=$10$*$exp(-6000$/$1.987$*$(1$/$450$-$1$/$T))$
page-pf11
12-57$
P12-10)(b))Continued$
$
$
$
)
P12-10)(c)$
For$a$co-current$heat$exchanger,$
page-pf12
12-58$
P12-10)(c)$continued$
See$Polymath$program$P12-10-c.pol.$
Calculated)values)of)the)DEQ)variables$
Variable)
initial)value)
minimal)value)
maximal)value)
final)value)
$V$
0$
0$
10$
10$
$X$
0$
0$
0.3611538$
0.3611538$
$T$
300$
300$
442.15965$
442.15965$
$Ta$
450$
434.90618$
450$
441.60853$
$k$
0.01$
0.01$
2.1999223$
2.1999223$
$Kc$
286.49665$
11.263546$
286.49665$
11.263546$
$Fa0$
0.2$
0.2$
0.2$
0.2$
$Ca0$
0.1$
0.1$
0.1$
0.1$
$ra$
-1.0E-04$
-0.0160802$
-1.0E-04$
-0.0019246$
$Xe$
0.8298116$
0.4023362$
0.8298116$
0.4023362$
$DH$
-6000$
-6000$
-6000$
-6000$
$Ua$
20$
20$
20$
20$
$Fao$
0.2$
0.2$
0.2$
0.2$
$sumcp$
30$
30$
30$
30$
$mc$
50$
50$
50$
50$
$Cpc$
1$
1$
1$
1$
$
ODE)Report)(RKF45)$
Differential$equations$as$entered$by$the$user$
$[1]$d(X)/d(V)$=$-ra$/$Fa0$
$Explicit$equations$as$entered$by$the$user$
$[1]$k$=$.01$*$exp((10000$/$1.987)$*$(1$/$300$-$1$/$T))$
$
Next$increase$the$coolant$flow$rate$and$run$the$same$program$to$compare$results.$
$
page-pf13
12-59$
P12-10)(d)$
For$counter-current$flow,$$
See$Polymath$program$P12-10-d.pol.$
Calculated)values)of)the)DEQ)variables$
Variable$
initial$value$
minimal$value$
maximal$value$
final$value$
$V$
0$
0$
10$
10$
$X$$
0$
0$
0.3647241$
0.3647241$
$T$
300$
300$
463.44558$
450.37724$
$Ta$
440.71$
440.71$
457.98124$
450.00189$
$k$$
0.01$
0.01$
3.7132516$
2.7077022$
$Kc$$
286.49665$
8.2274817$
286.49665$
9.9439517$
$Fa0$$
0.2$
$0.2$
0.2$
0.2$
$Ca0$
0.1$
0.1$
0.1$
$0.1$
$ra$
-1.0E-04$
-0.0256436$
-1.0E-04$
9.963E-04$
$Xe$$
0.8298116$
0.3488462$
0.8298116$
0.381006$
$DH$$
-6000$
-6000$
-6000$
-6000$
$Ua$$
20$
20$
20$
20$$
$Fao$
0.2$
0.2$
0.2$
0.2$
$sumcp$
30$
30$$
30$
30$
$Mc$
50$
50$
50$$
50$
$Cpc$
1$
1$
1$
1$
$
ODE)Report)(RKF45)$
Differential$equations$as$entered$by$the$user$
$[1]$d(X)/d(V)$=$-ra$/$Fa0$
$Explicit$equations$as$entered$by$the$user$
$[1]$k$=$.01$*$exp((10000$/$1.987)$*$(1$/$300$-$1$/$T))$
$
P12-10)(e)$
We$see$that$it$is$better$to$use$a$counter-current$coolant$flow$as$in$this$case$we$achieve$the$maximum$
page-pf14
12-60$
P12-10)(f)$
If$the$reaction$is$irreversible$but$endothermic,$we$have$$
$as$obtained$in$the$earlier$problem.$
See$Polymath$program$P12-10-f-co.pol.$
we$use$8-7f$co-current.pol$
Calculated)values)of)the)DEQ)variables$
Variable$
initial$value$
minimal$value$
maximal$value$
final$value$
$V$
0$
0$
10$
10$
$X$$
0$
0$
0.4016888$
0.4016888$
$T$
300$
300$
428.84625$
424.16715$
$Ta$
450$
425.45941$
450$
425.45941$
$K$
0.01$
0.01$
1.4951869$
1.314808$$
$Ca0$
0.1$
0.1$
0.1$
0.1$
$Fa0$
0.2$
0.2$
0.2$
0.2$
$Ra$
-1.0E-04$
$-0.0132694$
-1.0E-04$
-0.0047067$
$DH$
6000$
6000$
$6000$
6000$$
$Ua$
20$
20$
20$
20$
$Fao$
0.2$
0.2$
0.2$
0.2$
$sumcp$
30$
30$
30$
30$
$mc$
50$
50$
50$
50$
$Cpc$
1$
1$
1$
1$
$
ODE)Report)(RKF45)$
Differential$equations$as$entered$by$the$user$
$[1]$d(X)/d(V)$=$-ra$/$Fa0$
$Explicit$equations$as$entered$by$the$user$
$[1]$k$=$.01$*$exp((10000$/$2)$*$(1$/$300$-$1$/$T))$
$[2]$Ca0$=$0.1$
$[10]$Cpc$=$1$
$
$

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