{VERSION 1 1 "MS-Windows" "1.0"}{GLOBALS 1 2}{FONT 0 "" "" "Helve
tica-Bold" 7 10 0 "Helvetica-Bold" 10{COLOR "ff0000"}}{FONT 1 "Ti
mes New Roman" "Times New Roman" "Times-Roman" 4 12 64 "Times-Rom
an" 12{COLOR "000000"}}{FONT 2 "Courier New" "Courier New" "Couri
er" 4 10 192 "Courier" 10{COLOR "000000"}}{SCP_R 0 0 23{SCP_R 1 0
 3{COM_R 3 0{TEXT 1 34 "Tubular Reactor: Material Balances"}}
{COM_R 6 0{TEXT 1 0 ""}}{COM_R 9 0{TEXT 1 254 "The purpose of thi
s worksheet is to present the component material balances for a t
ubular reactor that make them amenable to solution.  These soluti
ons will often be obtained numerically although in some cases it 
is possible to find analytical solutions."}}}{SCP_R 11 0 2{INP_R 
13 0 "> "{TEXT 0 51 "restart; interface(labelling=false): printle
vel:=2:"}}{OUT_R 16 0 13{TEXT 2 1 "\012"}}}{SCP_R 18 0 1{COM_R 20
 0{TEXT 1 79 "The component material balances for a tubular react
or may be written as follows"}}}{SCP_R 22 0 2{INP_R 24 0 "> "
{TEXT 0 37 "CMB[i]:=Diff(F[i],z)=-R[i]*A: CMB[i];"}}{OUT_R 27 
8192 24{DAG =3(3n4\`Diff`,3b3n3\`F`,2n3\`i`n3\`z`+3*5b3n3\`R`p9j2
x0001n3\`A`p14i2x0001}}}{SCP_R 29 0 1{COM_R 31 0{TEXT 1 5 "where"
}}}{SCP_R 33 0 2{INP_R 35 0 "> "{TEXT 0 14 "'F[i],R[i],A';"}}
{OUT_R 38 8192 35{DAG ,4b3n3\`F`,2n3\`i`b3n3\`R`p4n3\`A`}}}{SCP_R
 40 0 3{COM_R 42 0{TEXT 1 145 "are, respectively, the molar flows
 of component i, the rate of reaction of component i  per unit vo
lume and the cross sectional area of the tube."}}{COM_R 45 0{TEXT
 1 0 ""}}{COM_R 48 0{TEXT 1 98 "The total material balance which 
is obtained by summing the component material balances as follows
"}}}{SCP_R 50 0 2{INP_R 52 0 "> "{TEXT 0 47 "TMB:=Diff(F[t],z)=su
m(rhs(CMB[i]),i=1..c): TMB;"}}{OUT_R 55 8192 52{DAG =3(3n4\`Diff`
,3b3n3\`F`,2n3\`t`n3\`z`(3n3\`sum`,3+3*5b3n3\`R`,2n3\`i`j2x0001n3
\`A`p1Ai2x0001=3p18~3p1An3\`c`}}}{SCP_R 57 0 1{COM_R 59 0{TEXT 1 
5 "where"}}}{SCP_R 61 0 2{INP_R 63 0 "> "{TEXT 0 22 "F[t]=sum(F[i
],i=1..c);"}}{OUT_R 66 8192 63{DAG =3b3n3\`F`,2n3\`t`(3n3\`sum`,3
b3p2,2n3\`i`=3pE~3j2x0001n3\`c`}}}{SCP_R 68 0 1{COM_R 70 0{TEXT 1
 41 "is the total molar flow of the mixture.  "}}}{SCP_R 72 0 2
{COM_R 74 0{TEXT 1 0 ""}}{COM_R 77 0{TEXT 1 221 "In some cases it
 will be easier to integrate the differential material balance eq
uations if we express them in terms of the total flow and mole fr
actions which are related to the component flow by the following 
definition"}}}{SCP_R 79 0 2{INP_R 81 0 "> "{TEXT 0 35 "FlowDefn:=
F[i]=F[t]*x[i]: FlowDefn;"}}{OUT_R 84 8192 81{DAG =3b3n3\`F`,2n3\
`i`*5b3p2,2n3\`t`j2x0001b3n3\`x`p4pD}}}{SCP_R 86 0 1{COM_R 88 0
{TEXT 1 77 "We may eliminate the component flow from the material
 balance equation to get"}}}{SCP_R 90 0 2{INP_R 92 0 "> "{TEXT 0 
38 "CMB[i]:=subs(FlowDefn,CMB[i]): CMB[i];"}}{OUT_R 95 8192 92
{DAG =3(3n4\`Diff`,3*5b3n3\`F`,2n3\`t`j2x0001b3n3\`x`,2n3\`i`pDn3
\`z`+3*5b3n3\`R`p12pDn3\`A`pDi2x0001}}}{SCP_R 97 0 1{COM_R 99 0
{TEXT 1 172 "This differential equation involves the differentiat
ion of a product for which we shall need the chain rule.  This is
 done in the next set of steps using Maple's D operator"}}}{SCP_R
 101 0 2{INP_R 103 0 "> "{TEXT 0 42 "t2:=subs(lhs(CMB[i])=D(F[t]*
x[i]),CMB[i]);"}}{OUT_R 106 8192 103{DAG :3n3\`t2`=3+5*5(3n3\`D`,
2b3n3\`F`,2n3\`t`j2x0001b3n3\`x`,2n3\`i`p10p10*5pAp10(3p7,2p12p10
p10+3*5b3n3\`R`p15p10n3\`A`p10i2x0001}}}{SCP_R 108 0 2{INP_R 110 
0 "> "{TEXT 0 26 "D(x[i])=solve(t2,D(x[i]));"}}{OUT_R 113 8192 
110{DAG =3(3n3\`D`,2b3n3\`x`,2n3\`i`+3*5+5*5(3p2,2b3n3\`F`,2n3\`t
`j2x0001p5p18p18*5b3n3\`R`p8p18n3\`A`p18p18p18p12i2x0001p29}}}
{SCP_R 115 0 2{INP_R 117 0 "> "{TEXT 0 68 "CMB[i]:=subs(\{D(F[t])
=Diff(F[t],z),D(x[i])=Diff(x[i],z)\},\"): CMB[i];"}}{OUT_R 120 
8192 117{DAG =3(3n4\`Diff`,3b3n3\`x`,2n3\`i`n3\`z`+3*5+5*5(3p2,3b
3n3\`F`,2n3\`t`pCj2x0001p6p1Cp1C*5b3n3\`R`p9p1Cn3\`A`p1Cp1Cp1Cp15
i2x0001p2D}}}{SCP_R 122 0 1{COM_R 124 0{TEXT 1 95 "The derivative
 of the total molar flow can be eliminated using the total materi
al balance above"}}}{SCP_R 126 0 2{INP_R 128 0 "> "{TEXT 0 33 "CM
B[i]:=subs(TMB,CMB[i]): CMB[i];"}}{OUT_R 131 8192 128{DAG =3(3n4\
`Diff`,3b3n3\`x`,2n3\`i`n3\`z`+3*5+5*5(3n3\`sum`,3+3*5b3n3\`R`p9j
2x0001n3\`A`p1Ci2x0001=3pA~3p1Cn3\`c`p1Cp6p1Cp1Cp17p1Cp1Cb3n3\`F`
,2n3\`t`p21p21}}}{SCP_R 133 0 1{COM_R 135 0{TEXT 1 72 "An applica
tion of these equations is considered in a separate worksheet."}}
}{SCP_R 137 0 1{INP_R 139 0 "> "{TEXT 0 0 ""}}}}{END}

