Design of an indirect-fired falling-particle air preheater for MHD power generation
by Chris Dewey Jensen
A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE
in Chemical Engineering
Montana State University
© Copyright by Chris Dewey Jensen (1976)
Abstract:
A preliminary design for an indirect-fired falling-particle air preheater for a 400 MW (thermal) MHD
power generation plant was made.
The project was broken down into three major parts: material properties prediction, development of a
theoretical model, and capital and annual cost estimation of the overall design.
A theoretical model was developed for an indirect-fired cored-brick air preheater. Capital and annual
costs were estimated and compared to those of the falling-particle air preheater. It was found that
overall air preheat systems involving these two designs would have approximately the same capital
costs of ~ $44 x 10^6, and annual costs of ~$6 x 10^6.
An economic comparison was then made between overall indirect-fired air preheat designs, and overall
direct-fired designs. In both the falling-particle and cored-brick cases, the capital cost of the
indirect-fired design was approximately 50% greater than the capital cost of the direct-fired design. STATEMENT OF PERMISSION TO COPY
In p re s e n tin g t h is
th e s is in p a r t i a l
f u l f i l l m e n t o f th e req u irem en ts
f o r an advanced degree a t Montana S ta te U n iv e r s it y , I a g ree t h a t th e
L ib r a r y s h a ll make i t
f r e e l y a v a ila b le f o r in s p e c tio n .
I f u r t h e r agree
t h a t p e rm is s io n f o r e x te n s iv e copying o f t h i s th e s is f o r s c h o la r ly
purposes may be g ra n te d by my m ajor p r o fe s s o r , o r , in h is absence, by th e
D ir e c t o r o f L i b r a r i e s .
o f th is
It
is understood t h a t any copying o r p u b lic a tio n
th e s is f o r f i n a n c ia l
g a in s h a ll
not be a llo w e d w ith o u t my w r it t e n
p e rm is s io n .
S ig n a tu re
Date
DESIGN OF AN INDIRECT-FIRED FALLING-PARTICLE AIR
PREHEATER FOR MHD POWER GENERATION
by
CHRIS DEWEY JENSEN
. A th e s is s u b m itted in p a r t i a l f u l f i l l m e n t
o f th e re q u ire m e n ts f o r th e degree
of ,
MASTER OF SCIENCE
in
Chemical E n g in e e rin g
Approved:
C h a irp e rs o n , G raduate Committee
Head, M a jo r Depactmght
Graduate?Dean
MONTANA STATE UNIVERSITY
Bozeman, Montana
A ugust, 1976
iii
ACKNOWLEDGMENT
The a u th o r w ishes to g iv e s p e c ia l
thanks to D r. W illia m G e n e tti
f o r h is in v a lu a b le s u p p o rt in th e developm ent o f t h i s p r o je c t .
S p e c ia l
thanks a ls o goes to D r. R. L . Mussulman o f th e M echanical
E n g in e e rin g D epartm ent o f . h i s many h e lp fu l s u g g e s tio n s .
The a u th o r g r a t e f u l l y acknowledges f i n a n c ia l s u p p o rt from
ERDA/MHD D iv is io n .
F i n a l l y , thanks goes to S h e rry G reene, s e c r e ta ry f o r th e Chemical
E n g in e e rin g D ep artm en t, f o r her ty p in g o f t h i s
th e s is .
iv
TABLE OF CONTENTS
Page
V IT A ............................
........................ ..............................................................................
.
ACKNOLWEDGMENTS ................................
ii
iii
L IS T OF TABLES...........................
v iii
L IS T OF FIGURES ............................................... ....
.......................................... ....
ix
NOMENCLATURE.............. ..........................................................
.
ABSTRACT.....................................
x
x ii
INTRODUCTION............................................
I
CONVENTIONAL TURBINE AND MHD POWER GENERATION.
............................
I
COMPARISON OF E F F IC IE N C IE S ...............................
4
THE NEED FOR PREHEATED A IR ...................................................................
5
DIRECT AND INDIRECT-FIRED AIR PREHEATERS . . .
i . . . . .
.
6
.
8
MODEL DEVELOPMENT AND DESIGN OF. FALLING-PARTICLE AIR PREHEATER. .
14
-GENERAL AIR PREHEATER D E S IG N ...........................
INTRODUCTION................... ^
.
PREDICTION OF MATERIAL PROPERTIES.
. . . . . . . . . . . . . . . .
14
14
GENERAL DESIGN CONSIDERATIONS............................................................................ 15
PARTICLE SIZE DISTRIBUTION ..............................................
16
PARTICLE TERMINAL VELOCITIES AND CHAMBER DIAMETER...................
.
17
DETERMINATION OF INSULATIONTHICKNESS............................................................ 17
OVERALL HEAT LOSS TO SURROUNDINGS.....................................
DEVELOPMENT OF MODEL DESIGN COMPUTER PROGRAM ........................
•
■
_
- - : v .
-•
' ,
-
.
;
18
. .
20
TABLE OF CONTENTS (C o n t ) .
Page
MODEL DEVELOPMENT AND DESIGN OF CORED-BRICK AIR PREHEATER.
COST SUMMARYFOR INDIRECT-FIRED AIR PREHEATERS
. . . .
21
. . . .................................... 23
FALLING-PARTICLE AIR PREHEATERS.......................
23
CORED-BRICK AIR PREHEATERS. ...........................................................................
24
FUEL SOURCES FOR INDIRECT-FIRED AIR PREHEATERS . . .
................................... 25
INTRODUCTION . .................................................................
25
COAL CARBONIZATION......................................................................................... ....
.
25
COAL G A S IF IC A T IO N .................................................................
26
OVERALL INDIRECT-FIRED AIR PREHEAT SYSTEMS COST COMPARISON . . . .
30
CAPITAL COST COMPARISON........................................
30
ANNUAL COST ESTIMATION.
30
....................................................................................
COMMENTS. ...........................................................................................................................33
CAPITAL COST COMPARISON OF DIRECT AND INDIRECT-FIRED AIR
PREHEAT SYSTEMS.
................... ... ...................
. . . .
.......................................... ....
33
COMMENTS...........................
33
;APPENDICES ......................................................................
APPENDIX
'
A:
35
PREDICTION OF MATERIAL PROPERTIES. . . . . .
1.
CONSTITUENTS OF.COAL GAS, MOLE %.
2.
PRODUCTS OF COAL GAS COMBUSTION ........................................................
3.
HOT
4.
EXHAUST"GAS PROPERTIES...,
HOT AIR PROPERTIES.
.-.
36
. . . . . . . . .
. . . ..
. . .. . .
.
36
36
.
............................................................
-V
................., ' - ' i
. •.
____
................
37
38
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v
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•
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TABLE OF CONTENTS(Cont).
Page
5.
ALUMINA PARTICLE PROPERTIES.............................................. ....
6.
INSULATION DATA.
7.
MHD COAL EXHAUST GAS PROPERTIES.
.3 8
.........................................................................................
. . .................................
39
GENERAL DESIGN BALANCES................................. ................................
41
1.
COMPOSITION OF MONTANA SUB-BITUMINOUS COAL ............................
41
2.
AIR INPUT TO 400 MW(T) MHD COMBUSTOR..........................................
41
3.
HEAT TRANSFER RATE TO AIR IN PREHEATER ......................................
42
APPENDIX B:
APPENDIX C:
. .
38
MODEL DEVELOPMENT OF FALLING-PARTICLE AIR PREHEATER.
43
1.
PARTICLE SIZE DISTRIBUTIONS.
.............................................................
2.
TERMINAL VELOCITY AND CHAMBER DIAMETER CALCULATION. . .
43
3.
DETERMINATION OF INSULATION THICKNESS. ■. . .
45
4.
WALL HEAT LOSS DETERMINATION................... ...• . . .. .......................
5.
OVERALL HEAT LOSS DETERMINATION..................................................
6.
DEVELOPMENT OF DESIGN EQUATIONS.
7.
DEFINITIONS OF PROGRAM VARIABLES AND PROGRAMLISTING
. . . . .
. .
43
. ■. .
47
47
............................
.
.
49
53
APPENDIX D:
MODEL DEVELOPMENT.OF CORED-BRICK AIR PREHEATER . . .
65
APPENDIX E:
COST PREDICTION FOR FALLING-PARTICLE AIR.PREHEATER .
72
. I.
INSULATION COSTS,.
. .
.. .........................'.......................................
2.
STEEL COLUMN COST.
3.
ALUMINA PARTICLE COST...........................................................74
4.
MISCELLANEOUS CAPITAL COSTS
.
72
72
74
v ii
TABLE OF CONTENTS (C o n t ) .
Page
5.
ESTIMATION OF ANNUAL MAINTENANCE COSTS
APPENDIX F:
.
COST PREDICTION FOR CORED-BRICK AIR PREHEATER. . . .
INSULATION COSTS ............................................................. ..........................
76
2.
STEEL COLUMN C O S TS ................... \........................................ ..
76
3.
CORED-BRICK COST.
77
4.
MISCELLANEOUS CAPITAL C O S T S ..................................... ......................
77
5.
ESTIMATION OF ANNUAL MAINTENANCE COSTS.....................................
78
I.
DESIGN DATA
............................................... ....
FOR.COAL CARBONIZATION SYSTEM . . . . .
MASS AND ENERGY.
APPENDIX H:
79
BALANCES..............................
DESIGN DATA
79
FOR COAL GASIFICATION SYSTEM. . . . . .
1.
MASS AND ENERGY
2.
CAPITAL AND ANNUAL COST PREDICTION..............................................
81
BALANCES............................................... ......
BIBLIOGRAPHY . . . . . . . . .
•
76
1.
APPENDIX G:
•
75
81
82
..................... ..............................................................
.
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83
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........... X
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v iii
L IS T OF TABLES
TABLE
PAGE
I
FALLING-PARTICLE CHAMBER DIMENSIONS............................ ............................21
II
CORED-BRICK CHAMBER DIMENSIONS .
III
ESTIMATED CAPITAL COST OF AN INDIRECT-FIRED FALLING-
.
. . . .
.
. .
. ...................
22
PARTICLE AIR PREHEATER .................................................................................23
IV
ESTIMATED CAPITAL COST OF AN INDI RECT-FI RED COREDBRICK.AIR PREHEATER...........................
V
COST COMPARISON OF OVERALL INDIRECT-FIRED COREDBRICK AND FALLING-PARTICLE AIR
VI
24
PREHEAT SYSTEMS...................31
CAPITAL COST COMPARISON OF DIRECT AND INDIRECT-FIRED
AIR PREHEAT SYSTEMS.
..................................................................
. . .
c.
• - •• V
,*
.
,.
33
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A , •» „ • ’ ‘
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ix
LIS T OF FIGURES
FIGURE
1
PAGE
CONVENTIONAL TURBINE AND MHD POWER GENERATION
SYSTEMS COMPARISONS....................................................
2
2
COMPARISON OF DIRECT AND INDIRECT-FIRED AIR PREHEAT
SYSTEMS...........................
7
3
CROSS-SECTION OF A CORED-BRICK AIR PREHEATER .................................
IO
4
SIM PLIFIED SCHEMATIC OF FALLING-PARTICLE AIR PREHEATER
12
5
COLUMN INSULATION CROSS-SECTION.
6
AIR PREHEAT SYSTEM WITH COAL CARBONIZER AS FUEL SOURCE
. . .
27
7
AIR PREHEAT SYSTEM WITH COAL GASIFIER AS FUEL SOURCE . . . .
28
8
ENTHALPY OF MHD COAL EXHAUST GAS v s . TEMPERATURE.................... 40
. . . .
.
. . .
. .......................................19
X
■
NOMENCLATURE
(E xclu d es te rm in o lo g y used e x c lu s iv e ly in computer program .
See Appendix
C -7 f o r d e f i n i t i o n s o f program v a r i a b l e s ) .
EXPLANATION
SYMBOL
A
AC
cD
cP
0C
Fd
nT
UNITS
p a r t i c l e s u rfa c e a re a
ft2
p a r t i c l e c r o s s -s e c tio n a l a re a
ft2
drag c o e f f i c i e n t
dim en sionless
s p e c if ic h e a t (c o n s ta n t p re s s u re )
BTUZlbm0F
in s id e column d ia m e te r
ft
drag fo rc e
Ib f
to ta l
number o f ho les in c o r e d -b r ic k
col umn
dim en sionless
Nu
N u s s e lt number, hD/k
Pr
P ra n d tl number, C m/k
P
"
. dim en sionless
R
h e a t t r a n s f e r r e s is ta n c e
°F hr/BTU
Re
Reynolds number, Du^p/y
dim en sionless
St
S ta n to n number, Nu/RePr
dim ensionless
TW
o u ts id e w a ll
te m p e ratu re
. °R
p a r t i c l e te m p e ra tu re
°R
V
gas te m p e ra tu re
°R
T=
am bient te m p e ra tu re
°R
TS
uO
do
o v e r a ll h e a t t r a n s f e r c o e f f i c i e n t
h o le d ia m e te r in c o r e d -b r ic k
B T U Z h rft2oF
ft
Xl
NOMENCLATURE (C o n t)
EXPLANATION
SYMBOL
p a r tic le
d ia m e te r
f
fr ic tio n
fa c to r
g
a c c e le r a tio n o f g r a v it y
dP
g r a v ita tio n a l
9c
c o n s ta n t, 3 2 .1 7
UNITS
ft
d im en sio n less
ft /s e c 2
5'
f t l b m/ l b f sec
h
c o n v e c tiv e h e a t t r a n s f e r c o e f f i c i e n t
B T U Z h rft2oF
k
therm al c o n d u c tiv ity
B T U Z h rft0F
q
h e a t t r a n s f e r r a te
uA
uT
V
.
BTUZhr
gas v e lo c it y
ftZ s e c
p a r t i c l e te rm in a l v e lo c it y
ftZ s e c
p a r t i c l e v e lo c it y
ftZ s e c
gas mass flo w r a te
Ib mZhr
p a r t i c l e mass flo w r a te
I b mZbr ’
“g
wS
X
v e r t ic a l
5
in s u la t io n th ic k n e s s
U
v is c o s it y
pg
ps
0 .
TW
d is ta n c e from to p o f column
ft
ft
lb Z fts e c
gas d e n s ity
1V
p a r t i c l e d e n s ity
Ib mZ f t 3
tim e
shear s tre s s a t w a ll
AX
in c re m e n ta l change in X
ZIP
p re ss u re drop
ft3
sec
Ib f Z ft2
ft
Ib p Z in 2
ABSTRACT
(
A p r e lim in a r y design f o r an i n d i r e c t - f i r e d f a l l i n g - p a r t i c l e a i r
p re h e a te r f o r a 400 MW (t h e r m a l) MHD power g e n e ra tio n p la n t was made.
The p r o je c t was broken down in t o th re e m ajo r p a r ts :
m a te r ia l p ro p e rtie s
p r e d ic t io n , developm ent o f a t h e o r e t ic a l m odel, and c a p it a l and annual
c o s t e s tim a tio n o f th e o v e r a ll d e s ig n .
A t h e o r e t ic a l model was developed f o r an i n d i r e c t - f i r e d c o re d -b ric k
a i r p r e h e a te r .
C a p ita l and annual costs were e s tim a te d and compared to
those o f th e f a l l i n g - p a r t i c l e a i r p r e h e a te r .
It.w a s found t h a t o v e r a ll
a i r p re h e a t systems in v o lv in g these two designs would have a p p ro x im a te ly
th e same c a p it a l costs o f ~ $44 x 1 0 6 , and annual costs o f ^$6 x IO ^.
An economic comparison was then made between o v e r a ll i n d i r e c t - f i r e d
a i r p re h e a t d e s ig n s , and o v e r a ll d i r e c t - f i r e d d e s ig n s .
In both th e ...
f a l l i n g - p a r t i c l e and c o r e d -b r ic k c ases, th e c a p it a l c o s t o f th e i n d i r e c t f i r e d design was a p p ro x im a te ly 50% .g r e a t e r than the c a p it a l c o s t o f the
d i r e c t - f i r e d d e s ig n .
INTRODUCTION
CONVENTIONAL TURBINE AND MHD POWER GENERATION
Magnetohydrodynamic (MHD) power c o n versio n is a method o f g e n e ra tin g
e l e c t r i c i t y w ith fe a tu r e s s im i l a r to those o f a c o n v e n tio n a l steam
t u b r in e d riv e n g e n e ra to r.
These s i m i l a r i t i e s w i l l be d is c u s s e d , and then
fe a tu r e s p e c u lia r to MHD power con versio n w i l l
F ig u re I
illu s tr a te s
be d is c u s s e d .
a v e ry s im p l i f i e d steam tu r b in e d riv e n
g e n e ra to r and a MHD g e n e ra to r.
In th e case o f the steam tu rb in e g e n e ra to r,
th e th erm al energy o f h o t combustion products (form ed by th e b u rn in g o f
some f o s s il
to steam .
fu e l)
is tra n s fo rm e d in t o l a t e n t energy by v a p o riz in g w a te r
The tra n s fo rm a tio n to m echanical energy is accom plished by
expanding th e steam a g a in s t tu r b in e b la d e s .
r o ta te s a co n ductor (t h e a rm a tu re )
s ta to r).
F i n a l l y , th e tu r b in e s h a f t
in a s t a t io n a r y m agnetic f i e l d
(th e
As the lin e s o f m agnetic f l u x a re b ro k en , a n e t e le c tro m o tiv e
fo rc e and r e s u lt in g c u r r e n t flo w is c re a te d in accordance w ith F a rad a y 's
laws o f in d u c tio n .
I t should be p o in te d o u t t h a t th e w o rkin g gas in the
t u r b in e c o u ld be any h o t , high p re s s u re g a s, as w e ll as steam .
• The MHD power co n ve rs io n system has a number o f s i m i l a r i t i e s
-tu rb in e g e n e r a to r.
In th e MHD c a s e , th e conductor which breaks the lin e s
o f m agnetic fo rc e o f th e s t a t io n a r y m agnetic f i e l d
c o n d u c tin g f l u i d ,
co n d u c tin g f l u i d
to th e
u s u a lly a gas.
is a h o t , e l e c t r i c a l l y
Thus th e therm al energy o f th e
is tra n s fo rm e d d i r e c t l y to e l e c t r i c a l e n e rg y .
The
system c o n s is ts o f an expanding d u ct through which th e h o t gas flo w s ,
which is lin e d on two o p p o s ite s id e s w ith e le c tr o d e s .
The e le c tro d e s
■ 2 -
E le c tr ic a l
Thermal
K in e tic
Mechanical
Brushes
Arm ature
T u rb in e
S ta to r
Steam
Hot Combustion Products
E le c tr ic a l
Thermal
H ot Cond.
Exhaust
E le c tro d e s
E lec tro m a g n e t
FIGURE I .
CONVENTIONAL TURBINE AND MHD POWER GENERATION
SYSTEMS COMPARISONS
- 3 c a r r y th e c u r r e n t to th e e x te r n a l lo a d c i r c u i t in the same fashion*
as
th e brushes in th e c o n v e n tio n a l g e n e ra to r.
. I t should be noted here t h a t th e r o t a t io n a l m otion o f th e arm ature
in a c o n v e n tio n a l g e n e ra to r c re a te s a a lt e r n a t i n g c u r r e n t , whereas th e
co n tin u o u s m otion o f th e gas p a s t th e e le c tro d e s in an MHD g e n e ra to r
c r e a te s d i r e c t c u r r e n t .
The two types o f MHD systems p o s s ib le a re open c y c le and clo sed
c y c le .
In th e c lo sed c y c le case, th e conducting f l u i d
re g e n e ra te d through the use o f h e a t e xch an g ers.
o f system a re c y c le s in v o lv in g
is re c y c le d and
Examples o f t h i s ty p e
noble g a se s , and l i q u i d m e ta ls .
In the
open c y c le c a s e , th e co n d u ctin g f l u i d passes through th e MHD d u c t o n ly
once.
S in ce t h i s
paper is d ir e c te d tow ard th e design o f h e a t exchange
components f o r open c y c le d f o s s i l - f u e l e d MHD systems th e c lo s e d c y c le
system w i l l
n o t be discussed f u r t h e r .
In an open c y c le MHD system , th e h o t gas (com bustion products o f
some f o s s i l
fu e l)
is made an e l e c t r i c a l
s ee d , such as KgO o r KgCOg.
conductor by th e a d d itio n o f a
The low io n iz a t io n p o te n tia l o f th e seed
en ab les a f r e e flo w o f e le c tr o n s w it h in th e gas.
th is
typ e is c a lle d a plasm a.
The e l e c t r i c a l
^ c o n d u c tin g
gas o f
c o n d u c tiv ity o f th e gas is
a r e l a t i v e measure o f th e ease in which th e gas w i l l conduct e l e c t r i c i t y .
The optimum seed c o n c e n tra tio n is about 1-5% b y .w e ig h t ( 1 , 2 ) .
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COMPARISON OF EFFICIENCIES
In th e ty p e o f power co n ve rs io n systems discussed so f a r ,
therm o­
dynamic e f f i c ie n c y is o p tim iz e d by m axim izing th e te m p e ra tu re o f th e
w o rkin g gas.
The presence o f h ig h ly s tre s s e d moving p a rts in a tu r b in e
g e n e ra to r becomes th e l i m i t i n g f a c t o r in th e w orking gas te m p e ra tu re ,
and thus in th e g e n e ra to r e f f i c i e n c y .
tr ic a l
As a r e s u l t o f t h i s , th e e le c ­
e f f i c i e n c i e s o b ta in e d in c o n v e n tio n a l steam tu r b in e power p la n ts
is between 30-45% .
In th e case o f MHD system s, no moving o r h ig h ly
s tre s s e d p a rts a re p re s e n t, and a l l
e x te r n a l
c o o lin g .
p a rts a re r e a d ily a c c e s s ib le to
Thus th e l i m i t i n g
f a c t o r in MHD e f f i c i e n c y is th e
te m p e ra tu re o f th e w orking gas i t s e l f , which can be much h ig h e r than th e
maximum te m p e ra tu re in a t u r b in e .
It
is fo re s e e n t h a t w orking gas
. te m p e ratu re s as h ig h as 5 0 0 0 -6 0 0 0 °F a re p o s s ib le f o r MHD a p p lic a t io n s .
E f f i c i e n c i e s o f systems em ploying p re s e n t te c h n o lo g y are p re d ic te d to be
about 50%.
as 60%.
Advanced systems a re fo re s e e n to have e f f i c i e n c i e s
as high
As a f u r t h e r comparison th e average e f f i c ie n c y o f a n u c le a r
f i s s i o n power g e n e ra tin g f a c i l i t y
is
32%.
Thus an advanced MHD p la n t
would have 1 .5 tim es the. e f f i c i e n c y o f a c o n v e n tio n a l steam tu r b in e p la n t,
and 1 ,9 tim e s th e e f f i c ie n c y o f a c o n v e n tio n a l n u c le a r p la n t .
I t should
be noted here t h a t th e advantage o f an MHD system is n o t is high e f f i ­
c ie n c y a lo n e , b u t i t s
a b ility
to c o n v e rt therm al to e l e c t r i c a l
in much h ig h e r te m p e ra tu re ranges th a n tu r b in e g e n e ra to rs .
energy
As a r e s u l t ,
th e exhaust gases from th e MHD d u c t would be tr a n s f e r r e d t o . a conven-
- 5 .t io n a l
gas o r steam tu r b in e g e n e ra tin g f a c i l i t y ,
The t o t a l
o r "bottom ing" p la n t .
power o u tp u t o f t h e . f a c i l i t y . w o u l d be about e v e n ly d iv id e d
between th e MHD -p la n t and the b ottom in g p la n t ( 1 , 3 ) .
THE NEED FOR PREHEATED AIR
The w o rking gas te m p e ratu re s necessary f o r e f f i c i e n t MHD power
g e n e ra tio n a re w e ll above gas te m p e ratu re s a c c e s s ib le .b y c o n v e n tio n a l
com bustion methods.
The combustion o f coal W ith am bient a i r g ives a
maximum te m p e ra tu re o f about 3 00 0 °F .
However, e f f i c i e n t MHD power
g e n e ra tio n re q u ire s a te m p e ra tu re o f about SOOO0F.
a v a ila b le in a c h ie v in g t h i s te m p e ra tu re .
oxygen.
Two methods a re
The f i r s t is th e use o f excess
In view o f th e high c o s t o f a f a c i l i t y
capable o f producing
th e amounts o f oxygen which would be necessary f o r a commercial s c a le
MHD i n s t a l l a t i o n , t h i s method is looked upon as uneconom ical w ith p re s e n t
te c h n o lo g y .
The second method in v o lv e s p re h e a tin g th e combustion a i r
b e fo re i t
used to burn th e c o a l.
is
e x t e n s iv e ly in th e s te e l
in d u s tr y .
T h is method has been used
C o n ven tio n al tube and s h e ll h e a t
exchangers can be used to p re h e a t a i r to about 1 70 0 °F .
To reach th e
te m p e ra tu re necessary f o r MHD power g e n e r a tio n , an a i r p re h e a t tem per­
a tu r e o f ab o u t SlOO0F is r e q u ir e d .
needed which w i l l
Thus a h e a t exchange system is
r a is e th e te m p e ra tu re o f a i r from 1 7 0 0 °F to 310 0 °F .
A number o f systems a re p r e s e n tly b e in g looked a t .
V-
.w
_-
, . '
.A .*
‘ -S'/..?
•
I'
V.... ■ •
-... V/
. . .-v -
.■
..
w . v -V . ! ...... .
■■■•
■■■
-
6
-
DIRECT AND INDIRECT-FIRED AIR PREHEATERS '
A i r p re h e a te rs a re o f two b a s ic ty p e s a cc o rd in g to how th e y f i t
i n t o th e o v e r a ll MHD process - d i r e c t - f i r e d and i n d i r e c t - f i r e d , as shown
in F ig u re 2 .
The d i r e c t - f i r e d
a i r p re h e a te r u t i l i z e s
th e therm al energy
o f th e MHD exh au st gas, which le a v e s th e MHD d u c t a t about 3 3 0 0 °F , to
d i r e c t l y p re h e a t a i r .
The i n d i r e c t - f i r e d a i r p re h e a te r u t i l i z e s
the
th e rm a l energy o f exhaust from a s e p a r a te ly f i r e d c le a n fu e l combustor
to p re h e a t th e combustion a i r .
d is a d v a n ta g e s .
The d i r e c t - f i r e d design has th re e b a s ic
F i r s t , th e MHD exh au st is
s la g , both o f which a re h ig h ly c o r r o s iv e .
laden w ith v a p o riz e d seed and
Second, as th e exh a u s t gas
t r a n s fe r s h e a t in t h e . a i r p r e h e a te r , both th e seed and s la g condense,
c o a tin g th e in t e r n a l works o f th e p r e h e a te r .
This s o lid re s id u e would
have to be c o n tin u o u s ly removed, not o n ly from an o p e ra tio n s s ta n d p o in t,
b u t a ls o because th e c o s t o f th e seed makes re c y c le im p e r a tiv e .
T h ir d ,
th e i n l e t p ressu re to th e MHD d u c t must be ~8 atm in o rd e r t h a t th e gas
can push i t s e l f through the d u c t.
As a r e s u l t o f t h i s , th e p reheated
com bustion a i r must be p re s s u riz e d to 8 atm .
p re s s u re from th e MHD d u c t is
d iffe r e n tia l
atm.
However, th e o u t l e t
Thus, th e re w i l l
be a pressure
o f ^6 % atm . between th e exh a u s t gas s id e and th e a i r s id e
o f th e p r e h e a te r .
d is a d v a n ta g e s .
a re e n c o u n te re d .
The i n d i r e c t - f i r e d a i r p re h e a te r has none o f these
S in c e .th e fu e l is c le a n , no problems w ith seed and s la g
A ls o , s in c e th e i n l e t p ressu re o f th e combustion
products o f th e fu e l can be a r b i t r a r i l y
:• .... V -:, .-V;
v .. ■:-> V:.
s e t , the h o t gas s id e and th e
-
. - v . v ; - v V v v v -
':V.;
Vv
- 7 Power Out
DIRECT-FIRED AIR PREHEATER
A ir
In v e r te r
Power Out
Steam
Supply
Heat
A ir
P reh e a t
MHD Duct
Feed A ir ^ lO O 0F
INDIRECT-FIRED AIR PREHEATER
FIGURE 2 .
Clean w
F u e l-Z -
P reheater
COMPARISON OF DIRECT AND INDIRECT-FIRED AIR
PREHEAT SYSTEMS
- 8 -
a i r s id e o f th e p re h e a te r can be run a t a 1 :1 pressure r a t i o .
The main
d is ad v a n ta g e o f th e i n d i r e c t - f . i r e d a i r p re h e a te r is t h a t , s in c e a
s e p a ra te c le a n fu e l must be employed, ~ 2 p o in ts in o v e r a ll c y c le
e ffic ie n c y w ill
be l o s t ( 5 , 8 ) .
A lso th e need f o r a c le a n fu e l
is a
d is a d v a n ta g e .
GENERAL AIR PREHEATER DESIGN
S ince c o n v e n tio n a l lo w -te m p e ra tu re h e a t exchange m a te r ia ls and
design a re in a d eq u a te f o r h ig h -te m p e ra tu re a i r p re h e a te r a p p lic a t io n s ,
new m a te r ia ls and designs must be c o n s id e re d .
M a te r ia ls most l i k e l y
to be a b le to w ith s ta n d h ig h -te m p e ra tu re c o rro s io n and therm al s tre s s
a re o f th e r e f r a c t o r y ty p e .
The m a te r ia l
used f o r th e h e a t - t r a n s f e r
medium should have a high therm al c o n d u c tiv ity and h e a t c a p a c ity fo r
e f f ic ie n t heat tra n s fe r.
The th re e most p o p u la r c a n d id a te s , in o rd e r
o f in c re a s in g c o s t, a re alum ina ( A ^ O g ) , magnesia (M gO ), and z ir c o n ia
(Z r O g ).
M a te r ia ls o f t h i s
ty p e a re employed in th e design o f both th e
h e a t t r a n s f e r medium and th e e x te r n a l
in s u la t io n o f th e a i r p re h e a te r.
O f th e many a i r p re h e a te r designs p r e s e n tly being re s e a rc h e d , two
w i l l be focused upon.
th e f a l l i n g - p a r t i c l e
These are the c o r e d -b r ic k a i r p r e h e a te r , and
a i r p r e h e a te r.
The c o r e d -b r ic k a i r p re h e a te r is b a s i c a ll y an in s u la te d column
packed w ith l o n g i t u d i n a ll y cored r e f r a c t o r y b ric k s o f high h e a t c a p a c ity .
A c r o s s -s e c tio n o f a t y p ic a l
c o r e d -b r ic k a i r p re h e a te r is shown in
- 9 F ig u re 3 .
The s e p a ra te b ric k s
a re o f hexagonal c ro s s -s e c tio n and th e
core d ia m e te r ranges from 0 .2 5 inches to 0 .7 5 inches ( 4 , 1 1 ) .
method o f o p e ra tio n is as fo llo w s :
The
th e a i r p re h e a te r column is s u it a b ly
v alv ed a t each end so t h a t h o t gas o r a i r can a l t e r n a t i v e l y be run
through th e column, in c o u n te rc u rre n t d ir e c t io n s .
In itia lly ,
b r ic k s a re heated f o r a s p e c ifie d p e rio d o f tim e by h o t.g a s .
is heated by ru n n in g i t
o f tim e .
th e cored
Then a i r
through .the colum n, a ls o f o r a s p e c ifie d amount
A problem is t h a t th e a i r o u tp u t is o f a c y c lic n a tu r e , w h ile
th e MHD process re q u ire s a c o n s ta n t flo w r a te o f combustion a i r .
T h is
problem is s o lv e d .b y th e use o f a number o f c o r e d -b r ic k a i r p re h e a te rs
o p e ra tin g in a c o ntinuous c y c le to o u tp u t a c o n s ta n t a i r flo w r a t e and
te m p e ra tu re .
The g r e a t e s t amount o f h e a t t r a n s f e r p e r u n it volume
(and th e r e f o r e th e h ig h e s t a i r p re h e a t te m p e ra tu re ) is o b ta in e d w ith
th e s m a lle s t flo w passage d ia m e te r, 0 .2 5 in c h e s .
problem in th e i n d i r e c t - f i r e d c as e .
T h is p re s e n ts no
However, in the d i r e c t - f i r e d
case,
c lo g g in g o f th e flo w passages by condensing seed and s la g re q u ire s t h a t
th e passage d ia m e te r be on th e o rd e r o f 0 .7 5 inches f o r e f f e c t i v e
o p e r a tio n .
Thus, f o r a g iv en a i r p re h e a t te m p e ra tu re , th e d i r e c t - f i r e d
a i r p re h e a te r w i l l
be o f c o n s id e ra b ly l a r g e r . s i z e th a n th e i n d i r e c t -
f i r e d a i r p r e h e a te r .
An im p o rta n t p o in t is t h a t therm al expansion o f
r e f r a c t o r y m a te r ia ls in th e s e te m p e ra tu re ranges is c o n s id e ra b le , and
must be accounted f o r in th e o v e r a ll column design ( 4 , 5 ) .
The f a l l i n g - p a r t i c l e
a i r p re h e a te r is shown by s im p l i f i e d schem atic
- 10 CORED ERICK MATRIX CONFIGURATION
1/4 INCH DIAMETER HOLE
O _ O
O _ O
O
FIGURE 3.
-o
CROSS-SECTION OF A CORED-BRICK AIR PREHEATER
- 11 in F ig u re 4 .
th e o th e r .
The design c o n s is ts o f two v e r t i c a l colum ns, one above
Small
0 .0 5 inch d ia m e te r) r e f r a c t o r y p a r t i c l e s
fa ll
through th e upper chamber, a re h e ld up a t th e in t e r f a c e between the
cham bers, and then f a l l
through th e lower, chamber.
The p a r t i c l e s are
th en r e tu rn e d to th e to p o f th e upper chamber by a pneum atic b lo w e r,
co m p letin g th e c y c le .
A t th e to p o f each chamber is a d i s t r i b u t o r
p la t e which spreads th e p a r t i c l e s e v e n ly across th e chamber d ia m e te r.
Hot gas (th e h e a tin g f l u i d )
e n te rs th e bottom o f th e upper chamber,
flo w s up th e chamber c o u n te rc u rre n t to th e flo w o f p a r t i c l e s , and e x it s
a t th e to p o f th e chamber through an exh au st m a n ifo ld ..
As th e gas
flo w s p a s t th e p a r t i c l e s , therm al energy is t r a n s fe r r e d to th e p a r t i c l e s .
In s im i l a r fa s h io n , a i r e n te rs the bottom o f th e lo w er chamber, flow s
upward c o u n te rc u rre n t to th e p a r t i c l e f lo w , and e x it s
m a n ifo ld .
through an exhaust
As th e a i r flo w s p a s t th e heated p a r t i c l e s , therm al energy
is t r a n s fe r r e d to th e a i r .
It
should be noted here t h a t th e design shown
in F ig u re 4 is s p e c if ic f o r th e i n d i r e c t - f i r e d c as e .
S ince both the
upper and lo w e r chambers a re a t n e a r ly th e same p re ss u re (~ 8 a tm ),
th e w e ig h t o f a number o f f e e t o f p a r t i c l e s
a t th e i n t e r f a c e between
th e chambers should o f f s e t any lea k ag e o f a i r o r hot gas.
However,
s in c e such a la r g e p re s s u re d i f f e r e n t i a l e x is ts between th e upper and
lo w er chambers in th e d i r e c t - f i r e d
c a s e , a complex v a lv in g mechanism o f
some s o r t must be d evised to p e rm it continuous flo w o f p a r t i c l e s
th e upper to lo w e r chamber, and m in im ize a i r ,le a k a g e .
from
U n lik e th e c o re d -
- 12 Exhaust Gas
P ~ 8 atm .
C lean Comb. Gas
T ~ 3500°F
A i r to MHD
M i-T e m p e ratu re
Pneumatic
Blow er
A ir
In le t
FIGURE 4 .
SIM PLIFIED SCHEMATIC OF FALLING-PARTICLE AIR
PREHEATER
- 13 b r ic k a i r p r e h e a te r , th e f a l l i n g
p a r t i c l e a i r p re h e a te r is a continuous
p ro c e s s , o u tp u ttin g a c o n s ta n t flo w r a t e and te m p e ratu re o f combustion
a ir .
Thus, c y c lic o p e ra tio n and i t s
complex v a lv in g a re unnecessary.
MODEL DEVELOPMENT AND DESIGN OF
FALLING-PARTICLE AIR .'PREHEATER
INTRODUCTION
A t h e o r e t ic a l model o f th e f a l l i n g
assembled on computer by W. E. G e n e t t i.
p a r t i c l e a i r p r e h e a te r was
A p r e lim in a r y design was then
made based on th e r e s u lt s o f th e model d a ta .
c a l l y w ith th e design o f an i n d i r e c t - f i r e d
h e a te r.
fa llin g
A ls o , a design f o r an i n d i r e c t - f i r e d
was made.
v ie w p o in t.
T h is th e s is d e a ls s p e c i f i ­
p a r t i c l e a i r p re ­
c o r e d -b r ic k a i r p re h e a te r
The two designs a re compared from both a s t r u c t u r a l and c o s t
In a d d it io n , a co st t r a d e o f f a n a ly s is is made f o r both th e
f a l l i n g - p a r t i c l e and c o r e d -b r ic k designs between th e i n d i r e c t - f i r e d and
th e d i r e c t - f i r e d
c ases.
Design and c o s t d a ta f o r d i r e c t - f i r e d
a ir
p re h e a te rs were p ro v id ed by W. E. G e n e tti and R. L . Mussulman.
PREDICTION OF MATERIAL PROPERTIES
As a p re lu d e to model developm ent o f th e a i r p r e h e a te r , e q u atio n s
were developed to p r e d ic t th e g e n era l p r o p e r tie s o f th e m a te r ia ls in v o lv e d
in th e d esig n f o r th e necessary te m p e ra tu re and p re ss u re ra n g e s .
m a te r ia ls in c lu d e th e h o t exh au st gases (h e a tin g f l u i d ) , a i r
f l u i d ) , fa llin g
(h e a te d
r e f r a c t o r y p a r t i c l e s , and i n s u la t io n .
As m entioned e a r l i e r , a s e p a ra te c le a n fu e l
a i r . p r e h e a te r .
The
This fu e l could be f u e l o i l ,
produced from th e d e v o l a t i l i z a t i o n . o f c o a l.
a v a i l a b i l i t y o f fu e l o i l and n a tu ra l
is n e e d e d .to f i r e
n a tu ra l
th e
g as, o r a fu e l
In view o f th e c o s t and
g a s, a fu e l produced from coal
- 15 d e v o l a t i l i z a t i o n was c a lle d f o r in th e o r ig in a l d e s ig n .
T h is fu e l
is
produced by th e h e a tin g o f coal to around 2 0 0 0 °F in th e absence o f
a i r , d r iv in g o f f th e v o l a t i l e , m a tte r as a gas w ith a h e a tin g v a lu e o f
O
ab o u t 575 B T U /ft .
T h is process is a ls o c a lle d c a r b o n iz a tio n .
C a rb o n iz a tio n o f 2000 lb o f coal y ie ld s about 1 1 ,0 0 0 f t ^
p lu s about 1400 lb o f coke.
o f coal g a s,
The c o n s t itu te n ts o f th e coal gas and i t s
products o f combustion a re presen ted in Appendix A.
E q u atio ns f o r th e fo llo w in g g e n e ra l p r o p e r tie s f o r a i r and th e
h o t exh au st gases were developed:
and h e a t c a p a c it y , a l l
v is c o s it y , therm al c o n d u c tiv ity ,
as a fu n c tio n o f te m p e ra tu re , and d e n s ity as
a fu n c tio n o f te m p e ra tu re , and p re s s u re .
These e q u a tio n s , along
w ith o th e r p e r t in e n t m a te r ia l p r o p e r tie s a re presented in Appendix A.
GENERAL DESIGN CONSIDERATIONS
A l l p re h e a te r desig n w o rk , both f o r t h i s r e p o r t and f o r th e G e n e t t iMussulman d e s ig n , was done on th e b a sis o f a 400 megawatt (th e rm a l) MHD
power g e n e ra tio n f a c i l i t y .
power in p u t to th e MHD .d u c t.
r e a c tio n and i t s
The th erm al power r a t in g is d e fin e d as th e
The s to ic h io m e try o f the. MHD combustion
r e la t e d mass b a lan c e s a re presen ted in Appendix B - I .
As
is evidenced by th e a i r re q u ire m e n t f o r th e combustion r e a c t i o n , th e a i r
p re h e a te r must supply 1 .2 7 9 .x IO 6 I b r a i r / h r to th e com bustor.
As p r e v i ­
o u s ly m e n tio n e d , th e te m p e ra tu re o f th e preh eated a i r m ust-be about SlOO0 F
-
16
-
S in ce c o n v e n tio n a l s h e ll-a n d -t u b e h e a t exchangers a re cap a b le o f producing
a i r te m p e ratu re s o f 1700 F , t h is is assumed to be th e a i r i n l e t te m p e ra tu re
o f th e a i r p r e h e a te r .
W ith these p aram eters s e t , th e h e a t t r a n s f e r r a t e
to th e a i r in th e p re h e a te r can be c a lc u la te d (Appendix B - 3 ) .
found to be 5 .1 5 5 x IO^ B T U /h r.
This was
I t should be noted a t t h i s p o in t t h a t
t h i s design f o r a 400 MW h eat.e x ch an g e f a c i l i t y
c a lls f o r th re e a i r
p re h e a te r colum ns, two running s im u lta n e o u s ly in p a r a l l e l , and one s p a re .
5
Thus, f o r one column, th e a i r flo w r a te would be 6 .3 9 5 x 10
I b / h r and
th e h e a t t r a n s f e r r a t e to th e a i r would be 2 .5 7 8 x 10^ B T U /h r.
PARTICLE SIZE DISTRIBUTION
The n e x t s te p in model development was to o b ta in a r e a l i s t i c
d i s t r i b u t i o n o f th e alum ina p a r t i c l e s .
s iz e
I t was found t h a t th e ta b u la r
alu m in a s to c k s u p p lie d by the Aluminum Company o f America would have to
be c l a s s i f i e d , narrow ing th e p a r t i c l e s iz e d i s t r i b u t i o n down to usable
ra n g e s .
Two p a r t i c l e s iz e ranges were in v e s tig a te d . . I n
th e la r g e s t p a r t i c l e d ia m e te r is 0 .0 5 i n .
The wide d i s t r i b u t i o n
0 .0 3 8 - 0 .0 5 i n . d ia m e te r, and the narrow d i s t r i b u t i o n
d ia m e te r.
e i t h e r case,
is
is 0 .0 4 2 - 0 .0 5 i n .
These d is t r ib u t io n s w i l l be r e f e r r e d to as "b lo w o u ts ", s in c e
any p a r t i c l e s m a lle r th an th e in c lu d e d range would blow o u t th e to p o f
th e chamber.
Appendix C -I .
These two p a r t i c l e s iz e d is t r ib u t io n s a re l i s t e d
in
- 17 PARTICLE TERMINAL VELOCITIES AND CHAMBER DIAMETER
The in s id e d ia m e te r o f th e chamber is a fu n c tio n o f th e te rm in a l
v e l o c i t y o f th e p a r t i c l e s .
The te rm in a l v e l o c i t y o f a p a r t i c l e
d e fin e d as t h a t v e lo c it y a t which th e f a l l i n g
is
p a r t i c l e stops a c c e le r a t in g .
In o th e r w o r d s ,s in c e drag in c re a s e s as v e lo c it y in c re a s e s , i t
is th e
maximum a t t a i n a b l e v e lo c it y o f th e p a r t i c l e
The
in a given f l u i d .
te rm in a l v e l o c i t i e s o f th e s m a lle s t p a r t i c l e s were c a lc u la t e d , sin ce
th e y would be th e f i r s t to “blow o u t" .
The maximum g a s .v e lo c it y ( a t
maximum te m p e ra tu re ) was then taken to be 100% o f t h i s te rm in a l v e l o c i t y .
Thus, s in c e th e a i r mass flo w r a t e is known, th e a i r chamber d ia m e te r
can be c a lc u la t e d .
These c a lc u la t io n s a re p resen ted in Appendix C -2 .
A t t h is p o in t , i t was i n i t i a l l y
were z e r o ; thus
= qga s -
assumed t h a t chamber h e a t losses
In t h is m anner, a gas mass flo w r a te was
found and gas chamber d ia m e te r c a lc u la t e d in analogous .fa s h io n to th e
a i r chamber d ia m e te r, as p re se n te d in Appendix C -2 .
r a te is 6 .5 2 x IO^ I b / h r .
The gas mass flo w
The in s id e dia m e te rs o f th e gas and a i r
chambers a r e , r e s p e c t iv e ly , 1 4 .2 f e e t and 1 1 .1 f e e t ( f o r th e 0 .0 4 2 inch
blow out c a s e ).
DETERMINATION OF INSULATION THICKNESS
The th ic k n e s s o f in s u la t io n needed to e f f e c t i v e l y in s u la t e th e
column was now d e te rm in e d .
P ro p e rtie s o f th e in s u la tio n
used are
p re se n te d in Appendix A -6 .
A t r i a l - a n d - e r r o r s o lu tio n to th e in s u la tio n
18 th ic k n e s s was made fo llo w in g
th e procedure presen ted in Appendix C -3 ,
w ith th e l i m i t i n g c o n d itio n t h a t th e maximum o u te r w a ll te m p e ra tu re
should n o t be above % 2 5 0 °F .
an o v e r a ll
The r e s u lt in g w a ll c r o s s -s e c t io n , having
th ic k n e s s o f 3 .5 f e e t ,
is shown in F ig u re 5 .
OVERALL HEAT LOSS TO SURROUNDINGS
W ith th e w a ll c ro s s -s e c tio n known, th e r a t e o f h e a t lo s s through
th e w a ll
can now be d e te rm in e d .
The h e a t t r a n s f e r e q u a tio n developed
in Appendix C -3 is used to f in d th e o u te r w a ll
v alu e s o f gas te m p e ra tu re .
Then (q /A ) loss is found a t each o f these
te m p e ra tu re s , and a curve is f i t
is
(q /A )i
te m p e ra tu re a t v a rio u s
as a fu n c tio n o f Tg.
to th e d a ta .
The r e s u lt in g eq u atio n
These c a lc u la t io n s a re r e la t e d in
Appendix C -4 .
O v e ra ll a i r p re h e a te r h e a t lo s se s can now be c a lc u la t e d .
o v e r a ll
The
lo sses are assumed to be the sum o f th e h e at losses in the a i r
and gas cham bers, p lu s th e h e a t lo s s from th e p a r t i c l e r e c y c le system .
The fo llo w in g two assum ptions must be made:
1.
The h e ig h ts o f th e gas and a i r chambers are 20 f e e t and
30 f e e t ,
2.
r e s p e c t iv e ly .
The h e a t lo s s from th e p a r t i c l e
re c y c le system is approxim ated
by th e a r it h m e t ic average o f th e h e a t losses from th e gas and
a i r chambers.
T h is p ro ced u re is o u tlin e d in Appendix C -5 .
W ith th e o v e r a ll h e a t
-
ro
(4 )
(3 )
r2
(2 )
^
(I)
r.
I
O u ter Wall
In n e r Wall
I
r3
19 -
3
................ -V T ^—
1 .1 2 5 f t
A r4
1 .1 2 5
ir 3
(I)
Norton AH-199B
(2 )
Norton AN-599
(3 )
J o h n s -M a n v ille JM -3000
(4 )
J o h n s -M a n v ille JM-23
FIGURE 5 .
-------------- t+ d ----------------- H
0 .7 5 f t
0 .5 0 f t
A r2
A r1
COLUMN INSULATION CROSS-SECTION
— 20 -
lo s s known, th e amount o f h e a t tr a n s fe r r e d from th e h o t gas to the
p a r tic le s
can be d e te rm in e d , and a r e f in e d v a lu e f o r th e gas e x i t
te m p e ra tu re is found to be 2 3 3 0 °F .
The average p a r t i c l e te m p e ra tu re
between th e chambers is assumed to be th e average o f th e bottom gas
te m p e ra tu re and th e to p a i r te m p e ra tu re , o r 3 30 0 °F .
te m p e ra tu re in th e p a r t i c l e
re c y c le system is
The average p a r t i c l e
s p e c ifie d to be th e average
o f th e to p gas te m p e ra tu re and th e bottom a i r te m p e ra tu re , o r 2 0 1 5 °F.
T h is method o f e s tim a tin g th e chamber h e ig h ts to a r r iv e a t th e o v e r a ll
h e a t lo sses is assumed to be r ig o r o u s , s in c e h e a t losses amount to o n ly
~ 0.2% o f th e t o t a l h e a t t r a n s f e r r a t e .
Now t h a t a l l
h e a t t r a n s f e r r a te s a re known, the p a r t i c l e mass flo w
r a t e is c a lc u la t e d to be 6 .5 4 x IO^ I b / h r .
DEVELOPMENT OF MODEL. DESIGN COMPUTER PROGRAM
A computer program was developed to a s s is t in th e p r e lim in a r y
design o f th e a i r p r e h e a te r .
The o p e ra tio n o f th e program in v o lv e s
th e s o lu tio n o f th re e sim ultaneous d i f f e r e n t i a l
b alan ce between p a r t i c l e s
e q u a tio n s :
and a i r across a d i f f e r e n t i a l
a momentum b a lan c e on a f a l l i n g
an energy
elem ent o f tim e ,
p a r t i c l e , and an o v e r a ll energy b a la n c e ,
in c lu d in g h e a t lo s s e s , across a d i f f e r e n t i a l
balan ces a r e developed in Appendix C -6 .
column e le m e n t.
D e f in it io n s o f a l l
These
program
v a r ia b le s , a program l i s t i n g , and a program o u tp u t are p re se n te d in
Appendix C -7 .
As can be s ee n , th e program o u tp u t g iv es a l i s t i n g o f
im p o r ta n t chamber parameters in .in c r e m e n t s o f h e i g h t , s t a r t i n g a t th e to p
o f th e gas o r a i r column and.moving down.
Based on t h i s data and data
a lr e a d y p re s e n te d , o v e r a l l chamber dimensions can be c a l c u l a t e d .
are l i s t e d
These
in T a b le I .
TABLE I .
FALLING PARTICLE CHAMBER DIMENSIONS
Gas Chamber
A i r Chamber
Blowout ( i n . )
.0 3 8
.042
.03 8
.042
In s id e D ia m eter ( f t )
1 5 .1
1 4 .2
1 1 .8 4
1 1.1
O utside D ia m eter ( f t )
2 2 .1
2 1 .2
1 8 .8 4
1 8.1
Chamber H e ig h t ( f t )
2 0 .5
1 4 .2
3 9 .8
3 0 .0
Gas Mass Flow Rate ( I b / h r )
6 .5 2 x l0 5
Max. Gas V e l o c i t y ( f t / s e c )
1 8 .9
6 .5 2 x l0 5
6 .3 9 5 x l0 5
2 1 .5
Gas I n l e t Temperature ( 0F)
3500
3500
Gas E x i t Temperature ( 0F)
2330
2330
1 8 .3 4
.
6 .3 9 5 x l0 5
2 0 .8 8
1700
1700
3100
3100
MODEL DEVELOPMENT AND DESIGN .OF CORED-BRICK. AIR PREHEATER
A model was developed to s i z e an i n d i r e c t - f i r e d cored b r i c k a i r
p r e h e a tin g system.
It
i s assumed t h a t a 400 megawatt (th e rm a l) power
g e n e r a tio n f a c i l i t y would r e q u i r e an a i r p r e h e a te r system c o n s is t in g o f
seven s e p a r a te cored b r i c k chambers, s i x on l i n e w i t h one s p a r e .
At
any given ti m e , two columns would be h e a t in g a i r o r be being heated by
-
h o t gas.
22 -
The model c o n s is ts o f an energy b a lance across a d i f f e r e n t i a l
elem ent o f chamber a r e a , assuming th e b r ic k s to be i s o t h e r m a l .
For the
i n d i r e c t - f i r e d c a s e , b r ic k s w i t h . 0 .2 5 inch d ia m e te r holes a re used.
T h is h o le s i z e giv es th e b r i c k s a c r o s s - s e c t io n a l
25%.
g e om etric p o r o s i t y o f
C o n v e ctiv e h e at t r a n s f e r data ( 1 7 ) f o r h e a t t r a n s f e r c o e f f i c i e n t s
i n c i r c u l a r tubes is used.
Pressure d ro p , as w e ll as volume, must be
o p tim iz e d t o g iv e th e b e s t d e s ig n .
Appendix D.
Model development i s p resented in
An i n s u l a t i o n th ic k n e s s o f 3 .5 ' f t
is assumed.
The chamber
dimensions r e s u l t i n g from t h i s model a re presented in T a b le I I .
TABLE I I .
CORED BRICK CHAMBER DIMENSIONS
Hole D iam eter ( i n . )
0 .2 5
O v e r a ll H e ig h t ( f t )
2 3 .3
In s id e D iam eter ( f t )
8 .9
O utside D iam eter ( f t )
15.9
AT
- A i r Flow ( 0F)
aV
155
AT
- Gas Flow ( 0F)
dv
100
Pressure Drop, psi
4 .4 3
. COST SUMMARY FOR IN D IR E C T-F IRED
• AIR PREHEATERS
FALLING-PARTICLE AIR PREHEATERS
C a p it a l
c o s t p r e d i c t i o n f o r th e i n d i r e c t - f i r e d f a l l i n g - p a r t i c l e a i r
p r e h e a te r is developed i n Appendix E..
o n ly .
T a b le I I I
These costs are f o r one u n i t
gives c o s t data f o r both, one u n i t and f o r an o v e r a l l
t h r e e - u n i t system.
TABLE I I I .
ESTIMATED CAPITAL COST OF INDIRECT-FIRED
FALLING-PARTICLE AIR PREHEATER
0 .0 3 8 i n . Blowout
U n i t Cost
T o ta l C o s t*
0 .0 4 2 in . Blowout
U n it Cost
T o ta l C ost*
$ 2 .2 7 x l0 6
$ 6 . S lx l O 6
$ 1 .7 2 x l0 6
$ 5 .2 x l0 6
1 .7 3 x l0 6
5 . ID x lO 6
1 .3 3 x l0 6
5 . OxlO6
Alumina P a r t i c l e s
.1 2 x l0 6
.3 6 x l0 6
.IB x lO 6
.4 5 x l0 6
P ip in g
.3 x l0 6
.D xlO 6
.S x lO 6
.DxlO 6
Valves
1 .3 6 x l0 5
.4 1 x l0 6
.IS B x lO 6
.4 1 x l0 6
S te e l
In s u la tio n
I n s tr u m e n t a t io n
S tru c tu re
TOTAL
* T o ta l Cost o f 3 u n it s
.S x lO 6
.S x lO 6
■ 6 .2 x l0 6
4 .7 x l0 6
2 0 .2 x l0 6
1 7 . OxlO6
.
/
- 24 CORED-BRICK AIR PREHEATERS
C a p ita l
costs f o r the c o r e d - b r ic k a i r p r e h e a te r system are
developed in Appendix F.
A g a in , th e s e f i g u r e s a re f o r one u n i t o n ly .
The o v e r a l l c o r e d - b r ic k a i r p r e h e a t e r system c o n s is ts o f seven u n i t s .
These costs a re summarized i n T able IV .
TABLE I V .
ESTIMATED CAPITAL COST OF INDIRECT-FIRED
CORED-BRICK AIR PREHEATER
U n i t Cost
T o ta l
Cost (7 u n i t s )
$ .21 6 X IO 6
$ 1 .5 1 x IO6
In s u la tio n
.662 X IO 6
4 . 6 3 x IO 6
Cored B r ic k
.552 X IO6
3 .8 6 x IO6
S te e l
P ip in g
Valves
I n s tr u m e n t a t io n
S tru c tu re
TOTAL
1 .1 x IO 6
.136 X IO 6
.9 5 x IO 6
. 3 x IO6
3 . 0 x IO6
$ 1 5 .4 x IO6
FUEL SOURCES F O R IN DIRECT-FIRED AIR PREHEATERS
INTRODUCTION
A complete i n d i r e c t - f i r e d a i r p r e h e a t e r system w i l l
in c lu d e a f u e l
source o f some s o r t .
n e c e s s a rily
Since the purpose o f i n d i r e c t - f i r e d
a i r p r e h e a t e r design i s t o g e t away from th e disadvantages o f using
th e seed and s la g - l a d e n MHD e xhaust gas as an energy s o u rc e , th e fu e l
should be c le a n and burn e f f i c i e n t l y .
under c o n s i d e r a t i o n a r e f u e l
The th r e e m ajor f u e l s p r e s e n t l y
o i l , n a tu r a l gas, and s y n t h e t i c gas made
from p a r t i a l I y o r c o m p le te ly g a s i f i e d c o a l .
c o s t and s c a r c i t y o f f u e l o i l
and n a t u r a l
However, in l i g h t o f the
gas, the c o s t o f running a
commercial s c a le i n d i r e c t - f i r e d a i r p r e h e a te r w i t h these m a t e r i a l s
would be p r o h i b i t i v e .
been c o n c e n tra te d upon.
Thus, th e p o s s i b i l i t y o f coal
g a s i f i c a t i o n has
Two b a s ic g a s i f i c a t i o n designs a r e c o n s id e re d ,
co al c a r b o n i z a t i o n and coal g a s i f i c a t i o n .
COAL CARBONIZATION
Coal c a r b o n i z a t i o n in v o lv e s th e h e a t in g o f coal in th e absence o f
a ir.
A t a te m p e ra tu re o f 1800 - 2 0 0 0 °F , the v o l a t i l e m a t t e r in the
coal i s d r iv e n o f f as an i n t e r m e d i ate-BTU f u e l
v a lu e o f a p p r o x im a te ly 550 B T U /ft^ ( 1 0 ) .
fu e l
gas, having a h e a tin g
I f t h i s gas co u ld be used to
th e a i r p r e h e a t e r , then coal would be th e s o le f u e l source o f the
o v e ra ll
power g e n e r a tio n complex.
The c a r b o n iz a t io n o f a ton o f coal
y i e l d s a p p r o x im a te ly 1 1,0 00 f t 3 o f t h i s f u e l gas plus about 1400 Ib ^
o f coke.
The coke b y -p ro d u c t would be mixed w i t h th e coal fe e d to
-
th e MHD combustor.
Mass and energy balances f o r t h i s system a re
pre se n te d i n Appendix G.
MHD exh a u s t gases.
F ig u re 6 .
26 -
The c a r b o n iz e r would b e .h e a te d by d i f f u s e d
A s i m p l i f i e d design o f th e system is shown in
The balances pre se n te d in Appendix G re v e a l t h a t , even i f
pure coke were used as th e s o le f u e l
source in th e MHD combustor, the
coke flo w r a t e from th e coal c a r b o n iz e r would be n e a r l y tw ic e the
necessary coke flo w r a t e t o th e MHD combustor.
a lo n e , th e use o f coal c a r b o n i z a t i o n t o f u e l
p r e h e a te r appears h i g h l y i n f e a s i b l e .
Thus, on t h i s ba sis
the i n d i r e c t - f i r e d a i r
Because o f t h i s ,
an economic
study o f coal c a r b o n i z a t i o n was n o t pursued.
COAL GASIFICATION
The p o s s i b i l i t y o f using g a s i f i e d coal as th e f u e l
i n d i r e c t - f i r e d a i r p r e h e a t system was i n v e s t i g a t e d .
g a s i f i c a t i o n o f coal t o s y n t h e t i c f u e l
source f o r th e
The complete
gas o f high BTU c o n te n t
( ~ 950 B T U /f t^ STD) in v o lv e s h e a t in g th e coal to g a s i f y th e v o l a t i l e
m a t t e r , s h i f t r e a c t i n g the carbon monoxide w i t h w a t e r to form hydrogen
and carbon d i o x i d e , removal o f HgS and COg, and f i n a l l y m ethanation
o f th e r e s u l t i n g gaseous m i x t u r e .
However, m ethanation o f th e CO-Hg
gas m ix tu r e has y e t to be c o m m erc ially dem onstrated.
g a s f i c i a t i o n system w i l l
Thus the
be p resented h e r e , b u t i t should be noted t h a t
progress is necessary b e fo r e the system i s t e c h n o l o g i c a l l y f e a s i b l e .
Data on th e system is pre se n te d i n Appendix H.
F ig u re 7 d e p ic t s a
- 27 -
Fuel
Gas
P reheate # _
T=1700
MHD Duct
Combustio
Chamber
FIGURE 6 .
AIR PREHEAT SYSTEM WITH COAL CARBONIZATION
AS FUEL SOURCE
To
Bottoming
P la n t
- 28
a
'
1700°F
G a s ifie r
Preheater
L. I .
MHD Duct
FIGURE 7.
AIR PREHEAT SYSTEM WITH COAL GASIFIER
AS FUEL SYSTEM
A ir
-
29 -
s i m p l i f i e d coal g a s i f i e r as th e f u e l
p re h ea te r.
source f o r an i n d i r e c t - f i r e d a i r
Data on th e p o s s i b i l i t y o f p a r t i a l char r e c y c le or o th e r
uses f o r c h ar was not a v a i l a b l e .
The p a r t i c u l a r g a s i f i c a t i o n process
i n v e s t i g a t e d i s th e CC^-acceptor p r o c e s s , as i t
c a p ita l
cost o f a l l
processes looked a t .
has th e lo w e s t o v e r a l l
However, i t
i s o n ly capable
o f g a s i f y i n g l i g n i t e and no n -c a kin g sub-bitum inous c o a l s .
Data was
n o t a v a i l a b l e on t h e f e a s i b i l i t y o f u t i H i z i n g Montana sub-bitum inous
coal in t h e CC^-acceptor process.
coal
As i s shown in Appendix H - l , the
flo w r a t e to th e g a s i f i e r would be about 47% o f th e t o t a l
f l o w r a t e t o th e power g e n e r a tin g complex.
The c a p i t a l
coal
c o s t f o r the
g a s i f i c a t i o n system i s e s tim a te d a t $ 2 7 .5 x 10^, w i t h an e s tim a te d
annual o p e r a t in g c o s t o f $ 4 . 3 x 106 ( 7 ) .
OVERALL INDIRECT-FIRED AIR PREHEAT
SYSTEMS COST COMPARISON
CAPITAL COST COMPARISON
As can be seen in comparing Tables I I I
and I V , the f a l l i n g - p a r t i c l e
p r e h e a te r ( 0 . 0 4 2 i n blow out) and th e c o r e d - b r ic k p r e h e a te r have n e a r l y
th e same c a p i t a l
co st,
v a r y in g b y . o n ly $ 1 .6 x 10®.
T h is i s w i t h i n th e
l i m i t s o f e s tim a te d accuracy f o r a .l o n g - r a n g e economic a n a l y s is o f
t h i s ty p e .
w ill
Assuming t h a t th e c a p i t a l
c o s t o f th e f u e l
be th e same f o r both a i r p r e h e a t systems, o v e r a l l
source system
system c a p i t a l
costs can now be e s t im a te d .
-ANNUAL COST ESTIMATION
An e s t im a te o f annual maintenance costs f o r th e a i r p r e h e a te r was
made.
The development o f th e s e costs is presented in Appendix E-5
f o r th e f a l l i n g - p a r t i c l e a i r p r e h e a t e r , and in Appendix F-5 f o r the
c o r e d - b r ic k a i r p r e h e a t e r .
I t should be noted t h a t th e s e f i g u r e s are
q u i t e rough e s t im a t e s , and should be weighed w ith a p p r o p r ia t e
s k e p t ic is m .
T a b le V pre se n ts an o v e r a l l c a p i t a l and annual cost
comparison f o r th e two i n d i r e c t - f i r e d a i r p re h e a t systems.
- 31 TABLE V.
■
COST COMPARISON OF OVERALL INDIRECT-FIRED
CORED-BRICK AND FALLING-PARTICLE AIR PRE­
HEAT SYSTEMS
C o r e d -B r ic k
A i r P r e h e a te r
P r e h e a te r C a p i t a l
Cost
$ 1 5 .4 x IO6
F a llin g -P a rtic le
A i r P re h e a te r
( 0 . 0 4 2 i n . Blowout)
$
1 7 .0 x IO6
Fuel Source C a p i t a l Cost
2 7 . 5 x IO6
2 7 . 5 x IO 6
TOTAL C a p i t a l
4 2 . 9 x IO 6
4 4 . 5 x IO 6
Cost
TOTAL Annual Cost
(in c lu d e s f u e l source)
$
5 . 8 x IO6
$
6 . 4 x IO 6
COMMENTS
A number o f im p o rta n t p o in ts should be made in c o n s id e r in g these
two o v e r a l l
1)
designs:
The l e v e l o f te c h n o lo g y o f th e c o r e d - b r ic k a i r p r e h e a te r design
i s much h ig h e r than t h a t o f th e f a l l i n g - p a r t i c l e
d e s ig n .
a i r p re h e a te r
The u t i l i t y o f th e c o r e d - b r ic k design has been
demonstrated i n a number o f a p p l i c a t i o n s , and an abundance
o f design d a ta i s a v a i l a b l e .
The f a l l i n g p a r t i c l e d e s ig n ,
however, has not y e t been dem onstrated.
2)
Since th e f a l l i n g - p a r t i c l e d e s ig n .o u tp u ts a s te a d y a i r flo w
r a t e a t a u n iform te m p e r a tu r e , o p e r a t io n o f th e MHD combustor
and duct would p ro b a b ly be smoother than w ith th e c y c l i c
-
32 -
o p e r a tio n s o f th e c o r e d - b r ic k d e s ig n .
3)
The need f o r c o n s t a n t - o p e r a t in g
w ill
v a lv e s in th e c o r e d - b r ic k
in c re a s e annual m aintenance costs as a r e s u l t o f v a lv e
breakdown and a t t r i t i o n .
v a lv e s w i l l
W ith th e f a l l i n g - p a r t i c l e
d e s ig n ,
be used o n ly f o r s t a r t u p , shutdown, and flo w r a t e
c o n tro l.
4)
P a r t i c l e replacem ent through a p p r o p r ia t e access p o r ts
(p ro b a b ly
i n th e p a r t i c l e r e c y c le system) i n th e f a l l i n g - p a r t i c l e
design w i l l
be a r e l a t i v e l y e f f o r t l e s s p ro c e d u re , r e q u i r i n g no
equipment shutdown and d i s m a n t l i n g .
C o r e d -b r ic k replacem ent
i n th e c o r e d - b r ic k d e s ig n , however, w i l l
shutdown and complete d is m a n t l i n g .
r e q u i r e column
CAPITAL COST COMPARISON OF DIRECT AND
INDIRECT-FIRED AIR PREHEAT SYSTEMS
C a p ita l
c o s t data f o r d i r e c t - f i r e d
c o r e d - b r ic k and f a l l i n g -
p a r t i c l e a i r . p re h e a t systems was s u p p lie d by W. E. G e n e tti and R. L.
Mussulman ( 1 2 ) .
These d a ta a re compared w i t h i n d i r e c t - f i r e d design
d a ta i n T a b le V I .
Only th e 0 .0 4 2 i n . blowout design o f t h e f a l l i n g -
p a r t i c l e a i r p r e h e a te r i s c o n s id e re d .
Annual c o s t d a ta f o r d i r e c t -
f i r e d a i r p r e h e a t systems was not a v a i l a b l e .
TABLE V I .
CAPITAL COST COMPARISON OF DIRECT AND
• ■ INDIRECT-FIRED AIR PREHEAT SYSTEMS
DIRECT-FIRED
O v e r a ll
C a p i t a l Cost
INDIRECT-FIRED
F a llin g -P a rt.
C o r e d -B ric k
F a llin g -P a rt.-
C o re d -B ric k
$ 3 0 .4 x IO6
$ 3 1 .3 x IO 6
$ 4 4 .5 x IO6
$ 4 2 .9 x IO 6
As can be seen, i n each design case th e c a p i t a l
f i r e d a i r p r e h e a t system i s about 75% o f t h e c a p i t a l
c o s t o f the d i r e c t c o s t o f th e
i n d i r e c t - f i r e d system.
COMMENTS
In comparing th e o v e r a l l designs o f d i r e c t and i n d i r e c t - f i r e d a i r
p r e h e a t systems, the f o l l o w i n g comments can be made:
I)
T o t a l coal f u e l costs f o r th e o v e r a l l
.
power g e n e r a tin g
complex w i t h th e i n d i r e c t - f i r e d a i r p re h e a t system w i l l
be
- 34 n e a r l y double those o f th e o v e r a l l
a i r p r e h e a t.
complex w i t h d i r e c t - f i r e d
However, s in c e the therm al energy o f th e MHD
exhaust gas w i t h i n d i r e c t - f i r e d a i r p r e h e a tin g i s not used t o
preheat a i r ,
a g r e a t e r percentage o f the t o t a l
t h e complex w i l l
power o u tp u t o f
be produced by th e bottom ing p l a n t .
In
a d d i t i o n , a l a r g e r bottom ing p l a n t would be a b le t o u t i l i z e
th e therm al energy o f th e exhaust gas l e a v in g th e i n d i r e c t f i r e d a i r p r e h e a t system.
2)
S ince th e environm ent w i t h i n th e d i r e c t - f i r e d system design
i s much more c o r r o s i v e than t h a t o f th e i n d i r e c t - f i r e d
system d e s ig n , annual maintenance costs can be expected to
be s u b s t a n t i a l l y h ig h e r w ith the d i r e c t - f i r e d system.
3)
A few p o in ts i n o v e r a l l
thermodynamic e f f i c i e n c y a r e l o s t in
th e power g e n e r a tin g complex using an i n d i r e c t - f i r e d
p r e h e a t s y s te m .( 5 , 8 ) .
a ir
APPENDICES
-
APPENDIX A:
I.
2.
36 -
PREDICTION OF MATERIAL PROPERTIES
C o n s titu e n ts o f Coal Gas, Mole %
CO
CO2
H2
N2
O2
CH^
8 .6
1 .5
5 2 .5
3 .5
0 .3
3 1 .4
H e a tin g V a lu e , B T U /ft^
575
Products o f Coal Gas Combustion
CO2
H2O
N2
Mole %
8 .7 7
2 1 .2 3
7 0 .0 0
W eight %
1 4 .1 5
14.01
7 1 .8 5
(A v e . M ol. W t. = 2 7 . 2 8 )
Flame Temp. = 3665°F
Notes on p r e d i c t i o n o f exhaust gas and a i r p r o p e r t i e s :
a)
V i s c o s i t y and therm al c o n d u c t i v i t y o f gaseous m ix tu re s were found
a t given te m p e ratu re s assuming t h a t :
pmix ~ I ^ i y i
- '
*Snix ~ |^i*S'
where y .. = mole f r a c t i o n o f component i .
V i s c o s i t i e s and thermal
c o n d u c t i v i t i e s were c a l c u l a t e d a t a number o f te m p e r a tu r e s .
d a ta were then f i t
t o th e f o l l o w i n g general e q u a tio n s :
B
- m i x * AT
b)
mix
The h e a t c a p a c i t y o f th e exhaust gas was assumed to"obey the
f o l l o w i n g e x p re s s io n :
m
+ X
twH2O cPH2O
+ Wr
'PC0,
The
-
37 -
w a t e r v a p o r, and carbon d i o x i d e , r e s p e c t i v e l y .
The X is a f a c t o r
in tro d u c e d t o account f o r d i s s o c i a t i o n o f HgO and COg in the gas a t
high te m p e r a tu r e s .
X i s e s tim a te d from h e a t c a p a c i t y data
c a l c u l a t e d f o r coal combustion gases and the com position o f such
gases.
S ince th e w e ig h t f r a c t i o n s and h e a t c a p a c i t i e s o f a l l
gas c o n s t i t u e n t s a re known, th e f a c t o r X can be c a l c u l a t e d a t
a number o f te m p eratu res
(1 5 ).
Cp^ was c a l c u l a t e d f o r a number o f te m p e ra tu re s , and a curve was
fit
t o th e r e s u l t i n g data ( 1 4 , 1 5 ) .
fo llo w e d by W. E. G e n e tti
A s i m i l a r procedure was
in d e ve lo p in g the h e a t c a p a c ity e q u atio n
fo r hot a i r .
c)
The Id e a l Gas Law is assumed a c c u r a te in th e d e n s it y e q u a tio n .
3.
Hot Exhaust Gas P r o p e r t ie s
• Temperature Range:
P = 3 7 . 4 P /T
T = °R ,
k = 1 .2 3 4 x 10
ii = 1 .5 2 x 10
2000 - 4000°F
- 4 r 778
- 7 -J-.684
P = ATM, p = l b m / f t 3
T=°R,
k=
B T U /h rft°F
T = °R ,
y = Ib m /fts e c
Cp = - . 0 2 6 0 + 5 .1 0 0 x IO "6 T + 2 .9 6 7 x IO- 8 T "2
T = °R
-
4.
38 -
Hot A i r P r o p e r t ie s
Temperature Range:
P = 3 9 .1 2 P /T
1500 - 3500°F
T = °R ,
Q -4 t .5 8 3
k = 4 .7 3 6 x TO
y = 6 .0 7 x 10
- 7 -J-.513
P = ATM,
p = l b m/ f t
T = °R ,
k = B T U Z h rft0F
T = °R ,
y = I b mZ f t s e c
3
C = .2261 + 2 .8 2 9 5 x IO - 5 T - 2 .2 8 6 x IO - 9 T2
P
T = °R ,
5.
Alumina ( P a r t i c l e )
Note:
Cp = BTUZlbm0F
P r o p e r t ie s
The alumina p a r t i c l e
used i n t h i s design i s a t a b u l a r
alumina pro d u c t o f th e Aluminum Company o f Am erica.
pure fused a lu m in a .
It
is 99.5%
The p a r t i c l e d ia m e te r range i s 0 .0 3 6 in -
0 .0 5 in .
P = 232 I b mZ f t
3
k = 2 .9 1 + 2 .9 1 8 x 10- 6 ( T - 2 7 6 0 ) 2 - 1 . 5 6 1 1 x 10- 1 2 ( T - 2 7 6 0 ) 4
T = °R ,
k = B T U Z h rft0F
Cp = .25667 + 1 .6 3 3 9 x IO - 5 T
6.
T = °R ,
Cp = BTUZlbm0F
I n s u l a t i o n Data
The i n s u l a t i o n i s o f f o u r b a s ic ty p e s .
A v c o -E v e r e tt Research L a b o r a t o r i e s ,
This d a ta was s u p p lie d by
I n c . , E v e r e t t , Mass ( 5 ) .
- 39 M fg .
(I)
Norton
Type
Thickness
in .
AH-199B
3
k,
B T U /h rft°F
■ C o s t, $ Z f t 3
1 .7 9
140
( 2 ) Norton
AN-599
4 .5
.894
120
( 3 ) J o h n s -M a n v ille
JM -3000
4 .5
.292
100
( 4 ) J o h n s -M a n v ille
JM-23
4 .5
.119
80
7.
MHD Coal Exhaust Gas P r o p e r t ie s
These p r o p e r t i e s o f th e exhaust gas from an MHD duct were
developed by W., E. G e n e t t i .
p = 4 0 .9 4 6 P/T
T = °R ,
P = ATM,
k = .000872
T=
k = B T U Z h rft0F
p = 6 .0 8 4 x 10
Cp = .848446 -
-7
jk
°R ,
T
' = °R,
I b mZ f t 3
p = I b mZ f t s e c
.0004834T + 1 .0 1 1 0 6 x IO - 7 T2
T = ° R,
8.
p =
F o llo w in g is a graph ■;
Cp == BTUZlbm0F
F ig u re 8,, o f e n th a lp y o f MHD coal exhaust
gas v s . te m p e r a tu re , e s tim a te d by Avco E v e r e t t Research L a b o r a to r ie s
In c .
40 -
1300
1200
1100
1000
900
800
700
600
500
400
300
200
100
0
500
1000
1500
Gas Temp -° K
8.
ENTHALPY OF MHD COAL EXHAUST GAS vs. TEMPERATURE
- 41 APPENDIX B:
I.
GENERAL DESIGN BALANCES
Composition o f Montana S ub-bitum inous Coal
P roxim ate A n a ly s is
(6 )
Weight P e rc e n t
(as r e c e i v e d )
M o is tu re
2 4 .3
V o l a t il e M a tte r
2 8 .6
F ixed Carbon
3 9 .6
Ash
7 .5
100.0
U lt im a t e A n a ly s is
(as r e c e iv e d )
Ash
7 .5
S u lfu r
0.8
Hydrogen
•
Carbon
.
6.1
5 2 .2
0.8
N itr o g e n
3 2 .6
Oxygen
100.0
H ig h e r H e a tin g Value
2.
8944 B TU /lb^
A i r I n p u t t o 400 MW (T h e rm a l) MHD Combustor
Heat In p u t = 400 x IO 6 W att
I
x
3 .4 1 4 BTU
h r w att
= 1 .3 6 5 6 x IO9 BTU/hr
■
lb
Coal Rate = 1 .3 6 5 6 x IO 9 BTU/hr x - g g ^ 'BTU = 1 ^527 x 1()5
_ 42 -
Formula f o r M o is tu re and Ash-Free C o a l :
CH. 8 ° . 0 8 N. 0 2 S .00 8
Combustion R e a ctio n :
CH. 8 ° . 0 8 N.0 2 S .00 8
+
1 .1 7 8 0 2
->
CO2 + .4 H2O + .02N0 + .OOSSO2
Assume m o le c u la r w e ig h t o f coal = 1 4 .6 2 (m o is tu re and a s h - f r e e )
A i r re q u ire m e n t f o r coal combustion:
1 .1 7 8 mole O2
mole coal
x
mole coal
1 4 .6 2 lb Coal
x
32 l b O9
_______ _ £
mole O2
100 lb A i r
21 lb O2
= 1 2 .2 8 lb A i r
l b coal (m o is tu r e -a s h f r e e )
The m oistu re and a s h - f r e e coal r a t e i s :
( 1 . 5 2 7 x IO5 ) ( . 6 8 2 ) = 1 .0 4 1 x IO 5 I b / h r
Thus, th e combustion a i r r a t e i s :
A i r Rate = 1.0 4 1 x IO5 l b coal
hr
= 1 .2 7 9 x IO5 lb
x
1 2 .2 8 lb a i r
l b coal
a ir/h r
H eat T r a n s f e r Rate to A i r i n P r e h e a te r
3100°F
qa i r
Wa i r
z ITOO0F
Cpa i r
1 .2 7 9 x IO u l b a i r
dT
x
4 0 3 .0 4 BTU
5 .1 5 5 x IO8 BTU/hr
- 43 -
APPENDIX C:
I.
MODEL DEVELOPMENT OF FALLING-PARTICLE AIR
P a r t i c l e S iz e D i s t r i b u t i o n
Blowout
No. F r a c t io n
0 .0 4 2 i n .
. D ia m e te r, i n .
0 .0 5
0 .0 1 1
0 .0 5
0 .0 1 8 2
0 .0 4 6
0 .1 2 8
0 .0 4 6
0 .1 0 3 3
0 .0 4 4
0 .2 5 6
0 .0 4 5
0 .2 0 6 7
0 .0 4 2
0 :2 5 6
0 .0 4 4
0 .1 5 5 0
0 .0 4 0
0 .1 9 3
0 .0 4 3 5
0 .1 0 3 4
0 .0 3 9
.0 .1 0 5
0 .0 4 3
0 .1 5 5 0
0 .0 3 7 5
0 .0 5 1
0 .0 4 2
0 .2 5 8 4
0 .0 3 8 i n .
D ia m e te r, i n .
2.
PREHEATER
Blowout
No. F r a c t io n
Term inal V e l o c i t y and Chamber D iam eter C a l c u l a t i o n
Term inal v e l o c i t y is c a l c u l a t e d using th e general e q u a tio n f o r
s p h e r ic a l
p a rtic le s
developed i n McCabe and S m ith , U n i t O perations
o f Chemical E n g in e e r in g , Second E d i t i o n , pp. 1 64 -1 6 9:
U uT
I
9 ps } 5 / 7
1 8 .5 }
3
Now, assuming t h a t
d8 / 7
2 /7
P
u
3 /7
m
u ;
= U j f o r th e s m a l l e s t p a r t i c l e a t the
h ig h e s t te m p e ra tu re :
(2)
Wa - UApA
A , WA/U Ap = , 0 . 2 / 4
D.
ir
(3 )
Ub . p
44 W ith a l l
gas p r o p e r t i e s e v a lu a te d a t th e h ig h e s t chamber
te m p e r a tu re .
A i r Chamber:
( p r o p e r t i e s e v a lu a te d a t T = 3560°R)
0 .0 3 8 i n . Blowout
Uy, f t / s e c
1 8 .3 4
As an i n i t i a l
- 0 .0 4 2 i n . Blowout
UA , f t / s e c
D i, f t
1 8 .3 4
1 1 .8 4
U y ,f t / s e c
‘ . 2 0 .8 8
U ^ ,f t / s e c
2 0 .8 8
D i, f t
1 1 .1
e s t i m a t e , no h e a t losses were assumed; thus
qa i r = qgas = 2 .5 7 8 x IO 8 BTU/hr
Gas Chamber:
To o b ta in th e gas mass f lo w r a t e
(w g ), the f o l l o w i n g e xpre s sion
was used:
3500°F
qgas = Wg -f ZSOO0F
CpG dT
The 2 3 0 0 °F e x i t te m p e ra tu re o f th e gas is a ls o an e s t i m a t e , which
w i l l s ubse que ntly be r e f i n e d .
From t h i s c a l c u l a t i o n ,
Wri = 6 .5 2 x IO 5 I b / h r
9
Now, i n analogous fa s h io n t o th e a i r chamber d ia m e te r c a l c u l a t i o n s
th e gas chamber d ia m e te r i s c a l c u l a t e d .
a t T = 3 5 0 0 °F .= 3 9 6 0 °R ).
(Gas p r o p e r t i e s a r e developed
45 -
0 .0 3 8 i n . Blowout
0 .0 4 2 i n . Blowout
Uy = Ug, f t / s e c
D ij f t .
1 3 .3 0
1 5 .1
Note:
• Uy = Ugj f t / s e c
D ij f t .
1 5 .1 4
1 4 .2
Since th e maximum te m p e ra tu re o f t h e . gas chamber occurs a t
th e bottom o f the chamber, t h i s i s where th e te r m in a l
c a l c u l a t i o n s were made.
v e lo c ity
However, s in c e v e l o c i t i e s a t t h e to p o f the
column a r e d e s ir e d ( t o be analogous to th e a i r column d a t a ) , th e above
v e l o c i t i e s a re a r e s u l t o f m u l t i p l y i n g th e bottom te r m in a l
by th e f a c t o r 2760oR /3 9 6 0 oR, assuming th e I d e a l
v e lo c itie s
Gas Law to ho ld i n t h i s
te m p e ratu re range.
3.
D e te r m in a tio n o f I n s u l a t i o n Thickness
The general e q u a tio n f o r h e a t t r a n s f e r between th e gas i n the
column and am bient a i r
is :
" ' V - Uo <Tg - U
(5 )
where
Tg = gas te m p e ratu re
Too = am bient a i r te m p e ratu re
Uq = o v e r a l l
h e a t t r a n s f e r c o e f f i c i e n t based on o u ts id e column area
q /A 0 = h e a t f l u x
D R,w a ll
( 6)
- 46 -
h. = in n e r w a ll
c o n v e c tiv e h e at t r a n s f e r c o e f f i c i e n t
h„ = o u te r w a ll c o n v e c tiv e h eat t r a n s f e r c o e f f i c i e n t
o
(7 )
'4
N a tu r a l c o n v e c tio n is assumed between th e o u te r w a ll
r e s i s t a n c e to heat t r a n s f e r o f th e s t e e l
and a i r .
The
s t r u c t u r e on th e o u ts id e o f
th e i n s u l a t i o n i s assumed small
r e l a t i v e to the i n s u l a t i o n r e s i s t a n c e ,
and i s n e g le c te d .
( 1 0 ) , th e c o r r e l a t i o n f o r th e o u te r
From P e r r y 's
c o n v e c tiv e h e at t r a n s f e r c o e f f i c i e n t i s :
1 /3
( 8)
H0 - 0 . 1 8 (Tw - T J
f o r GrPr > IO^
S ince Tw i s unknown, Tw is .n e e d e d as a fu n c t i o n o f T , the gas
te m p e ra tu re :
From e q u a tio n 6:
(9 )
Now, s in c e q/A Q = h0 (T w - Too) ,
(Tg
- U = —Sr—
<T„
t h i s can be equated t o e q u atio n 5:
-U
do)
-
47 -
S u b s t i t u t i n g e q u a tio n 9 i n t o e q u a tio n 10 g iv e s :
<Tg - T J
= ( I + h0(£ V
x^ M
( H)
T w -TJ
S u b s t i t u t i o n o f e q u a tio n 8 i n t o e q u a tio n 11 g i v e s :
4 /3
■ (Tg " U
- <TW - T J
+ -18 (Tw - T j
An
( =Rwa11 + ^ - )
(
12)
- or 4 /3
<Tg - T J = (Tw - T J
'I
ln (— )
where
+ - 18 ( T w - T J
ln (% -)
rI
w a ll
NOTE:
4.
In t h i s design h.
l n ( - % r — ).
+
(13)
( £Rwall +
- n A - +
i
i
ln (— z r~ )
-
r
]
is assumed t o be 10 B T U / h r f t ° F .
Wall Heat Loss D e te rm in a tio n
In itia lly ,
Tw i s found f o r v a r io u s values o f Tg using e q u atio n 12
in Appendix C -3 .
5 in Appendix C -3 .
Then ( cIZA)-Joss is found f o r these values using e q u a tio n
A curve i s then f i t
t o th e d a t a , r e s u l t i n g in
t h e f o l l o w i n g e q u a tio n :
( q / A ) i oss = - 4 4 . 9 + .0612 Tg ,
Tg = °R
(14)
( q / A ) i oss = B T U / h r f t 2
5.
O v e r a ll Heat Loss D e te rm in a tio n
Using e q u a tio n 14, an average h e a t lo s s i s found f o r each chamber:
- 48 -
(q /A ),
= 1 1 6 .3
La i r
h rft
(q /A ),
= 1 4 6 .3 —
Lgas
h rft^
Now, assuming t h a t L „ =c = 20 f t and L . = 30 f t and D
gaS
a lr
°gas
(1 4 .2 + 7 .0 ) = 2 1 .2 f t
= (QZA)1 1T(D0 ) ( L )
%
q.
, D
= ( 1 1 . 1 + 7 . 0 ) = 1 8 .1 f t
°a ir
(15)
= ( 1 4 6 . 3 ) (m )( 2 1 . 2 ) ( 2 0 ) = 1 .9 5 x IO5 BTU/hr
gas
q,
= ( 1 1 6 . 3 ) ( it) ( 1 8 . 1) (3 0 ) = 1 .9 8 x IO 5 BTU/hr
La i r
q,
= % ( 3 . 9 3 3 x IO 5 ) = 1 .9 7 x IO 5 BTU/hr
re c y c le
The o v e r a l l h e a t l o s s , then i s :
q,
^ o v e ra ll
= ( 1 . 9 5 + 1 .9 8 + 1 .9 7 ) x IO 5 = 5 . 9 x IO5 BTU/hr
An o v e r a l l energy balance g iv e s :
3960°R
ga i r + gIoss ~ ggas
^g
^T q
^Dgc*^
Tq i s the o n ly unknown i n t h i s e q u a tio n :
T =
O
2790°R = 2330°F
which agrees c l o s e l y w i t h th e o r i g i n a l e s t im a te f o r th e gas e x i t
te m p e ra tu re o f 2 30 0 °F .
An energy balance between th e s o l id s and th e a i r
i n th e a i r chamber g iv e s :
49 -
cIsoIids
(1 7 )
cIa ir +
a ir
3760°R
Cn dT = ( 2 . 5 7 8 x IO 8 + 1 .9 8 x IO 5 ) BTU/hr
Ps
Ws ^2475°R
which g iv e s Wg = 6 .5 4 x 10
6.
Ib /h r
Development o f Design Equations
Equations w i l l
be developed f o r th e a i r column; thus Tg > Tg a t
any p o i n t in th e column.
A ls o , i t
i s assumed t h a t X ( v e r t i c a l
p o s itio n )
equals 0 a t th e to p o f each column.
I)
Energy Balance Between P a r t i c l e s and A i r across D i f f e r e n t i a l
Time Element:
wSc Pst
S l e + i6 -
wS=P5t
where Ag = t o t a l
S I9 -
(1 8 )
- " V tS - V
s u r fa c e area o f p a r t i c l e s f a l l i n g
i n tim e
elem ent Ae
(Particle Vol. in ae) ( -s^
l flrea
Volume
)
p a rtic le
6W_
ie )(-
(1 9 )
d PpS
6
wScP5
- 6
<T, - Ts>
- 50 -
?Ts
C P TS rTS
Note:
In a l l
x -v e rtic a l
Ps
rlv
( 20)
(T 9 - V
design e q u a t i o n s , the independent v a r i a b l e is to be
d is ta n c e .
Thus, to tr a n s fo r m th e above e q u a t io n .
_ / dTs \ /
'
dT_
^ jQ
/
de \
'
H v
6h
d Pps cPsv
dx
( 21 )
de
*
" Ts^
( T h i s i s program s ta te m e n t 9 3 . 0 0 )
2)
X - D i r e c t i o n Momentum Balance on One P a r t i c l e :
ma.
2T ( x - d i r e c t i on fo r c e s )
mg
ma X = S -
de
where
- F.
Fd gc
TTdP3
TrdD
pS S - Fd9c
is th e drag fo r c e on th e p a r t i c l e
c ro s s -s e c tio n a l
From ( 9 ) ,
area.
( 22)
9
C d Pg ( V W ) 2 Ac
Fd = ------- - | g
(2 3 )
( 9 ) and Ac is th e p a r t i c l e
-
A3
a;
de
Pg(V+U)'
ps 9 ■ cC
3CPpg
g -
de
51 -
d 2g
A fi-
(2 4 )
(v+u)‘
4 dPpS
A g a in , s in ce th e independent v a r i a b l e x i s d e s i r e d .
de
de
_dV_
(2 5 )
de
__ g___________ 3CD °q (V+U)
dx
^
AdppgV
(26)
(program s ta te m e n t 9 5 .0 0 )
This e q u a t io n , when i n t e g r a t e d , giv es V as a fu n c t i o n o f x .
can be i n t e g r a t e d again t o g iv e e as a f u n c t i o n o f x:
de
=
dx
3)
I
V
O v e r a ll
(27)
(program s ta te m e n t 9 6 .0 0 )
Energy Balance Across D i f f e r e n t i a l Column Element AX:
T
In s u l.
In s u l.
X+AX
I
52
[WgCpg( T g " J r e f ^ x + A x
-
(q/A)[_ Ir (Dc + 26)
Ax
-
" Wg
gCpg
g " ^ e f j l X3
r g'( T g
=
- h s ( P a r t i c l e S u rfa c e Area i n Ax) (T 5 - T g)
(28)
where p a r t i c l e s u r fa c e area i n Ax
d- 2
V o l.
p a rtic le
de
GWsAx
6
de
P s dp
Thus, e q u a tio n 28 becomes
(q / A ) , ir(D
+ 26)
6 W5
- h,
-------------Now, s o l v i n g e q u a tio n 20 f o r
-W -
( Ts - Tg)
(2 9 )
(T 5- T g ) and s u b s t i t u t i n g t h i s v a lu e i n t o
e q u a tio n 29:
dT_
( q / A ) , ir(D +26 )
WsCps
(3 0 )
WgCpg
% %
The f i r s t term on th e r i g h t i n t h e above e q u a tio n i s la b e l e d XX
i n program s ta te m e n t 1 0 4 .0 0 .
program s ta te m e n t 9 9 . 0 0 .
The second term is la b e l e d YY ( 7 ) in
T h e i r sum and the r e s u l t i n g d i f f e r e n t i a l
e q u a tio n are program s ta te m e n t 105.00.
-
7.
D e f i n i t i o n s o f Program V a r ia b le s and Program L i s t i n g
(lis te d
in o r d e r o f appearance in program w i t h s ta te m e n t number)
Statem ent No.
M:
TEMPO:
4 .0 0
5 .0 0
53 -
- ' ,
s iz e it e r a t io n ' f o r p a r tic le s
(M = 1 - 7 )
gas te m p e ratu re a t to p o f chamber,°R
TP: . p a r t i c l e te m p e ra tu re a t to p o f chamber,°R
6 .0 0 ,7 .0 0
A , B : . c o n stan ts in gas v i s c o s i t y e q u a tio n
8 .0 0 ,9 .0 0
C,D:
c o n stan ts i n gas therm al c o n d u c t i v i t y e q u a tio n
1 0 .0 0
F:
c o n s ta n t i n gas d e n s i t y e q u a tio n
1 1 .0 0
P:
chamber p r e s s u r e , atm
1 2 .0 0
UG:
gas v e l c o i t y a t top o f chamber, f t / s e c
1 3 .0 0 ,1 4 .0 0
1 5 .0 0
AB ,BB5BC: ' constants in gas h e a t c a p a c ity e q u a tio n
1 6 .0 0
OS: . o v e r a l l
1 7 .0 0
WO:
1 8 .0 0
W:
chamber d ia m e te r ,
gas mass flo w r a t e ,
Ib /h r
p a r t i c l e mass flo w r a t e ,
2 0 . 0 0 - 2 6 . 0 0 DP(M):
d ia m e te r o f p a r t i c l e
3 1 . 0 0 - 3 7 . 0 0 FR(M):
number f r a c t i o n o f t o t a l
4 3 .0 0
. 10:
in te g r a t io n order
4 4 .0 0
. VP:
in itia l
45.
DO4 6 . 00
AA5AG:
in c lu d in g i n s u la t i o n , f t
Ib /h r
1M1, f t
p a r tic le s o f s iz e
p a r tic le v e lo c ity
constants in h e a t loss e q u a tio n
4 8 .0 0
V(M):
v e lo c ity o f p a r t i c l e o f s iz e
4 9 .0 0
T (M ):
t i m e , seconds
•j
1M1, f t / s e c
1M1
-
54 -
5 0 .0 0
TS(M):
te m p e ratu re o f p a r t i c l e s o f s i z e
5 5 .0 0
WS(M):
W *
FR(M) - - 7rD^M)3 p_
1M1 90R
W FR (M )D (M )'
7
WBlTl
Zc' FR(M)
M=I
= mass flo w r a t e o f p a r t i c l e s o f s i z e 1M1, I b / h r
7 9 .0 0
TG:
8 0 .0 0
DENG:
gas d e n s i t y , l b / f t ^
8 1 .0 0
DENS:
p a r t i c l e d e n s i t y , 232 l b / f t ^
8 2 .0 0
V IS:
8 3 .0 0
KG:
8 4 .0 0
U:
gas v e l o c i t y a t te m p e ra tu re TG, f t / s e c
8 5 .0 0
Gr
(V is c o s ity /d e n s ity )(3 6 0 0 ), f t ^ /h r
86.00
PR:
88.00
TH:
9 0 .0 0
R(M):
gas. te m p e r a tu re ,° R
gas v i s c o s i t y , I b ^ / f t s e c
gas therm al
c o n d u c tiv ity , B T U /h rft°F
(gas h e a t c a p a c i t y ) ( v i s o c i t y ) / ( c o n d u c t i v i t y ) , dimen­
s io n le s s
p a r t i c l e thermal c o n d u c t i v i t y , B T U / h r f t ° F
p a r t i c l e Reynolds number "of p a r t i c l e s i z e ,
1M ',
• dim ensionless
9 1 .0 0
H:
p a r t i c l e s u r fa c e c o n v e c tiv e h e a t t r a n s f e r c o e f f i c i e n t
B T U / h r f t ^ ° F , from:
9 2 .0 0
9 4 .0 0 9 4 .2 1
Z:
CD:
Nu = 0 . 2 R e ' ^ P r ^ ^
(R e fe re nce 13)
p a r t i c l e h e a t c a p a c i t y , BTUZlbm0F
drag c o e f f i c i e n t , dim ensionless
(th ree d iffe r e n t
. ■ e xpressions f o r drag c o e f f i c i e n t are g iven f o r th r e e
d i f f e r e n t ranges o f Reynolds number)
9 7 .0 0
YZ:
9 8 .0 0
S (M ):
gas h e a t c a p a c i t y , B T U /lb m°F
s t r e s s on p a r t i c l e o f s i z e
1M1, psi
-
9 9 .0 0
YY(M):
55 -
h e a t t r a n s f e r r a t e between p a r t i c l e s
o f s iz e
1M
and gas, BTU/hr
1 01.00
TEMPP( 7 ) :
w eig h ted average p a r t i c l e te m p e ra tu re f o r a l l
p a rtic le s
1 03 .00
Q:
q /A ( h e a t lo s s t o w a l l s per u n i t o u ts id e a r e a ) ,
B T U /h rft2
1 04.00
NOTE:
. XX:
t o t a l h e a t loss from chamber w a l l , BTU/hr
For i n f o r m a t i o n on general F o r tr a n fo rm a t and s u b r o u tin e s ,
see r e f e r e n c e ( 1 8 ) .
I* OOO
2. 000
3.000
4.000
4. 500
5.000
6.000
7.000
8. 000
9. 000
10.000
11.000
12.000
i3;ooo
14.000
15.000
16.000
17.000
18.000
19.000
20.000
21.000
22.000
23.000
24.000
25.000
26.000
31.000
32:000
33. 000
34:000
35:000
36:000
37:000
42.000
NAME LIST
DIMENSION. TSC7), V(7), WS(7), R(7), DTS(7), TEMPP(0:7)
1DV(7),T(7),DT(7),DP(7),S(7),FR(7),YY(0:7),UBC0:7)
TEMPO= 3560«
YY(O)=O.
T P = 3760.
A = . 000000607
B = . 513
C = :0004736
D = . 583
F= 39. 12
P= 8.
U G = 2 0 . 88
A B = . 2261
BB= . 000028295
B C = - . 000000002286
.DS= 18. I
UG= 6. 395E5
U = 6 . 54E5
REAL KG
DPC I) = .05/12
DPC 2 ) = . 046/12
DP C3)= . 0 4 5 / I2
DPC4)=.044/12
DP CS)=.0435/12
DP C6) = .043/12 .
DPyC 7) = . 042/12
FRC I)=.0182
FR C2) = . 1033
FR C3) = :20 67
F R C4) = . I550
FR C5) = « 1034
FR(6) = « I550
FR C7) = .2584
INPUT DX,X,PI,PF
43V000
44.000
45« OOO
46. OOO
47. OOO
48.OOO
49.000
50-000
51.000
52.OOO
53.000
54.000
55." 000
56 V OOO
57.000
58» 000
59.000
60.000
6 1."000
62.000
63.000
64.000
65.OOO
66.000
67.000
68.000
69.000
70.000
10=2
' VP=» I
149
12
I
900
901
902
903
A A = - 4 4 o9
A G = - 0612
D0 149 M= I* 7
V(M) = VP
T(M) = O.
TS(M)=TP
VB(O) = Oo
V B ( M ) = W B (M-I)+FR(M)*(DP(M)**3)
CONTINUE "
D0 12 M= I/ 7
WS(M)=FR(M)*(DP(M)**3)*V/VB(7)
CONTINUE
INPUT
WRITE ( 108, 900)
FO RMAT ( 'POSITION', 4X> *TS( I ) ', 7X, fTS (2) *, 7X,
I *TS(3) ', 7X, ^ 5 ( 4 ) r, 7X, rTS(S) r)
"WRITE” (108/901) F O R M A T < *TS (6) ", 7X, 'TS(7)',7X, 'TS( S ) ',7X, 'TS(9) ’, 7X,
l'TS(10)'/6X,'TS(ll)')
"WRITE (108, 902)
FORMAT ( 'GAS TEMP', 4X, 'V(I)', 8X# 'V(2) ', 8X, 'V(3)
8X,
I *V (4 ) ', 8X, 'V (5 ) ' ) ~
"WRITE (108,9035
_
FORMAT ( 'V(6) ', 8X, 'V(7) ', 8X, 'V(S) ', 8X, 'V(9) ', 8X,
I 'V ( I O ) ',7X,'V ( I l ) '5
"WR I T E " (108/904) "
I
\
9 06
FORfcAT C' STRESS ( I ) ' , 3 X
STRESS ( 2 ) ' , 3 X , ' STRESS ( 3 ) ' , 3 X ,
I ' STRESS C4 )* , 3 X V STRES'S ( 5 5* > 3 X * * STRESS ( 6 ) ' )
^R I TE ( 1 0 8 , 9 0 5 )
F ORfcAT ( ' S TRESS (7 ) ' , 3 X , ' S T R E S S ( 8 ) ' , 3 X , ' STRESS ( 9 ) ’ , 3 X ,
I * STRESS ( 1 0 ) ' , 2 X , ' S T R E S S ( 1 1 ) ' , 2 X , ' PRANDL NUf c ' )
WRI TE ( 1 0 8 , 9 0 6 )
FORf cATCf cAX REY NUfc' , I X , ' fcIN REY KU fc ' , I X , ' PART T E f c P ' , 3 X ,
7 8 .000
79 .000
80 . 0 0 0 2 0
81 . 0 0 0
82 . 0 0 0
83.000
84 . 0 0 0
85 . 0 0 0
86 . 0 0 0
87 . 0 0 0
88.000
89 . 0 0 0
90 . 0 0 0
91 . 0 0 0
92 . 0 0 0
93 . 0 0 0
93.100
93 . 2 0 0
94 . 0 0 0
94.100
94 . 2 0 0 9 9
94 . 2 0 5
94 . 2 1 0 8 0 0
9 4 . 3 0 0 98
95 . 0 0 0
I ' GAS V E L ' , 5 X , ' f c A X T I f c E ' , 4 X , ' f c I N T I f c E ' )
TG=TEfcPG
' '
DENG = F * ( P / T G )
DENS = 2 3 2 .
'
U IS = A * ( T G * * B )
HG =C * ( TG * * D )
U=UG * ( i’G /TEfcPG )
G = (A/C ) * ( T G * * ( B - D ) ) *3 600 •
PR=G*(AB+BB*TG+tiC*(TG**2 ) )
z DO 13 fc = l , 7
'
T H = 2 . 91 + ( 2 . 9 1 8 E - 6 ) * ( TS ( fc ) - 2 7 6 0 . ) * * 2
I - ( I .56 I I E -12 ) * ( T S (fc)-27 60 . ) * * 4
R ( M ) = D E NG * ( U +U (fc) ) * DP (fc ) / U IS
H = KG * ( . 2 * ( R ( f c ) * * . 7 ) * ( P R * * . 3 3 4 ) ) / D P ( M )
£ = • 2 5 6 6 7 + . 0 0 0 0 1 6 3 3 9 * r S (fc)
D T S (f c) = . 0 0 1 6 7 * h * ( T G - T S ( f c ) ) / ( D E N S * D P ( fc ) * Z * V ( M ) ) '
I F ( R ( M ) . LE .1 . ) , G 0 TO 9 9
I F ( R ( f c ) .GE . 5 0 0 . ) , G O TO. 8 0 0
CD = I 8 . 5 / ( H ( f c ) * * . 6 )
'
!
GO TO 98
CD= 2 4 . / R ( M )
'
GO TC 98
C D = . 44
I
i XXX —:0 •
DV ( f c ) = 3 2 .-17 / V ( f c ) - . 7 5 * C D * ( ( V( f c) +( J ) * * 2 ) *DE NG / (DENS * ( DP (fc ) )
7 I .000
7 2 .000
7 3. . 0 0 0
7 4 .000
75 . 0 0 0
7 6 .000
77 . 0 0 0
90^
905
* U CK ) )
96 . 0 0 0
97 . 0 0 0
98.000
99-000
100 . 0 0 0
101 . 0 0 0
102 . 0 0 0
103 . 0 0 0
I 04«000
I 05 . 0 0 0
I 06 . 0 0 0
107 . 0 0 0
108.000
109.000
I 10 . 0 0 0
I I I .000
I I 2 .000
I 13 . 0 0 0
I 14.000
I 15 - 0 0 0
I 16 . 0 0 0
I 17 . 0 0 0
I I 8.000
I I 9-000
120*000
121 . 0 0 0
1 22 . 0 0 0
DT ( M ) = I • /.V CM )
YZ=AB+BB *TG +BC* CTG * * 2 )
S ( M) =34 . 6 * H * D P < M ) * ( T S ( M ) - T G ) / T H
Y Y ( K ) = Y Y ( K - 1 ) +DTS ( M ) W S ( M ) * Z / (WG * Y Z )
PEMPP ( 0 ) = 0 •
TEMPP (M ) =TEt-PP ( M- V ) +WS ( M ) *TS ( M ) /W
13
COMP I MJE
Q = A A +AG =KTG+TEt - PP (7 ) ) / 2 •
XX = 3 . 1 4 * Q * D 5 / ( . v G * Y Z )
DTG = X X + Y Y (7 )
C AL L PHNPE (P I , P E , N E , X , TS ( I ) , TS ( 2 ) , TS ( 3 )
CALL PHN PR ( 0 , PS ( 6 ) , T S (7 ) , 0 . , 0 . , 0 . , 0 • )
C AL L P H N P H ( 0 , PG , V ( I ) , V ( 2 ) , V (3 ) , V ( 4 ) , V (5
C AL L P R^iT R ( 0 , U ( 6 ) , V (7 ) , 0 . , 0 • , 0 • , 0 • )
CALL PHNTR ( 0 , S ( I ) , S ( 2 ) , S ( 3 ) , S ( 4 ) , S ( 5 ) , S
CAL L P H N T H ( 0 , S (7 ) , 0 . , 0 . , D S , 0 • , 0 • )
CAL L PRNTR ( I , R ( I ) , R ( 7 ) , TEMPP (7 ) , J , T (7 ) , T
GO TC ( 1 0 0 , 1 ) , NE
100
, CAL L I NT I ( X , D X , I O )
'
DO 2 0 0 M= I , 7
C AL L I N T d S ( M ) , DPS ( M ) )
C AL L I N T ( V ( M ) , D V ( M ) )
CALL I N T C P ( M ) , D P ( M ) )
200 .
CONTI NUE
CAL L I NT (TG ,DPG )
G O TO 2 0
END
, TS ( 4 ) , TS ( 5 ) )
) )
(6))
(I ))
,
/
\
! F ORT 4 CD J
EXT . FORTRAN
OPTI ONS >NS
I U » VERSION F00
! RUN S J l L I B . 2 3 4
LINKING $
LINKING
: LIB
' P I * ASSOCIATED.
L I N K I N G ‘ SYSTEN L I B
? . 0 1 ^ 0 . j2 « ^ 4 0 .
?*
POS I T I ON
TS (I)
TS (7 )
TS ( 6 )
V (I)
GAS TENP
V (7 )
U (6 )
STRESS(2 )
STRESS( I )
STRESS(S)
STRESS (7 )
KAX REY NJN N I N R E Y - NUN
3 7 6 0 .0
.00000
376 0 .0
37 6 0 . 0
•10000
. 35 6 0 . 0
• I 0000
• I 0000
618.10
. 655 .25
•00000
57 9 . 9 6
160 . 26
190.79
I .9999
3529.0
3329.9
I .9146
1169.7
47 9 *0 9
240 .38
■
3 6 4 4 .0
3 4 8 0 .3
4.3615
I . 4 5 14
9 30 . 4 6
.00000
177 . 3 3
i
TS ( 2 )
TS(S)
V(2)
V(S)
STRESS( 3 )
STRESS( 9 )
PART TE NP
37 6 0 . 0
.00000
. 10000
.00000
6 0 8 .66
. .00000
3 76 0 .0
- 3 60 2 .0
.00000
/3.1250
.00000
85 2 . 0 6
.00000
3549-0
TS ( 3 )
TS ( 9 )
U (3 )
U (9 )
STRESS( 4 )
S TRESS ( 1 0 )
GAS UEL
376 0 .0
•00000
•I0000
•00000
TS ( 4 )
TS(10)
V (4)
^
V (10)
STRESS ( 5 )
STRESS( 1 1 )
NAX T I KE
376 0 .0
•00000
.10000
.00000
5 99*16
I 8-100
20.880
■
35 84 . 6
.00000
2 .7 5 25
•00000
7 5 8 .7 4
18.100
I 9*530
594.38
•00000
•10000
.00000
589.59
•00000
‘ 35 61 . 4
.00000
2 . 3 4 94 ■
.00000
703.78 •
,
•00000
.00000
•00000
*00000
2 . 4 8 10
TS ( 5 )
TS ( 11 )
V (5)
V(Il)
STRESS (6 )
PRANDL NUN
N I N T IKE
3 7 6 0 *0
.
3 5 4 6 .7
•00000
2.1359
.00000
640.93
.00000
.7 881 9
3 .9998
3406.9
3204.8
2 .5 887
1402 .5
535 .00
259-62
.
9.9993
3 1 3 6 .3
2 9 1 4 -7
4 .0916
1935 . 0
768*61
3 0 2 . 81
.
3 4 8 3 «6
3264.0
6 . 3 4 94
' 2 .6406
1180.1
. .00000
196.14 '
5.9996
3306-8
3 0 9 9 . 0 •'
3.1411
1592.1
608.64
275.10
7 .9995
3218.0
3 00 3 .5
3 .6348
1766 .3
6 87 . 9 2
289.21
3 5 6 1 .7
3360.2
5 .5544
2 .0975
I 064 • 6
•0 0000
I 87 . 1 2
■
'
/
•
3 4 0 7 .7
3178.6
6.. 9 7 5 0
■ 3 .1298
I 2 91 .7 I
.00000
204.95
3333.5
-3099.7
. 7 .5 0 95
3 . 5 8 40
' 1 4 0 2 .7
.00000
^ 2 1 3 .7 8
3498.2
.00000
3.9784
.00000
959.38
•00000
343 4 .2
3474.1
.00000
3 .5330
3404.9
.00000
4 . 5 9 80
.00000
I 057 .0
.00000
3 3 3 7 .1
3 3 7 7 .1
.00000
4.1227
•00000
921 «82
3318.0
.00000
5 .123 I
.00000
1 15 4 .5
•00000
3249.5
.
,
3 23 6 .0
.00000
5.5966
.00000
1252.9
•00000
3168.0
3 4 4 4 .2
•00000 ;
3 . 0 6 87
.00000
•00000
83 9 - 7 8
I 8.100 '
18.797
772.96
'
3426 .6
.00000
2 .8304
•00000
700 .3 8
.00000
»00000
3 .6124
1.1891
3 3 4 4 .6
«00000
3 «6361
.00000
84 8 • 92
3 3 2 6 .3
*00000
3 . 3 895
.00000
772.27
I 8.100
.00000
•00000
.1 8 . 1 7 6
. \
3288-3
.00000
4 .6334
.00000
I 007 .6
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- 65 -
APPENDIX D:
MODEL DEVELOPMENT OF CORED-BRICK AIR PREHEATER
B r ic k s a r e assumed i s o t h e r m a l .
w ith
The geom etric p o r o s i t y o f b r ic k s
. 2 5 - i n c h d ia m e te r holes is 25%.
AIR PREHEATER WITH DIFFERENTIAL ELEMENT:
Energy Balance o v e r D i f f e r e n t i a l
Element Ax:
h e a t i n p u t - heat o u tp u t = h e a t t r a n s f e r r e d to / f r o m b r ic k s
W 3 Ux - “gPgTglx "
where
Px = Trd0 N1 , N j = number o f holes i n c r o s s -s e c t io n
PT = ( T b r 1 Ck - Tg)
Note:
The f a c t o r 2 accounts f o r the f a c t t h a t , a t any g iv en tim e ,
gas w i l l
be flo w in g through two chambers.
<!>
- 66 -
wgCpg
5 i
-IK
(2 )
- 2hV T
l
(3 )
WgGPgdTg = ZhPxdXAT
D e fin in g Nu = hd^/k and i n t e g r a t i n g across the o v e r a l l
chamber le n g th
g iv e s :
W
- V
\
M
' - 2 (J v >
Cpr
.
%
px U T
(4 )
- V
2ATP„
Nu
E quation 4 can be w r i t t e n
in terms o f known dim enionless v a r i a b l e s :
UbPd0
W.
where U.
p Ak
Wg = gas mass flo w r a t e
Ab = t o t a l
c r o s s - s e c t io n a l area o f holes
Ab = 2(%)AC f o r a ge o m etric p o r o s i t y o f . 2 5 , f o r two chambers.
2W_
UbP
Ac = c r o s s - s e c t io n a l
area o f one chamber
%
CPq W
S u b s t i t u t i n g e q u a tio n s 5 and 6 i n t o e q u a tio n 4 g iv e s :
-
67 -
RePrAc (Tg^ - T ^ )
(7)
Nu
4PX AT
C r o s s - s e c t io n a l Area o f holes
_______ P o r o s it y __________________
■ P e r im e te r o f holes
(N t
1
TTdQ2 )
4
tV rd0
And, S t = S ta n to n Number =
Nu
do ' Tg2 - Tg1 )
\
L
(8 )
S t 4 AT
The o v e r a l l chamber le n g th
is c a l c u l a t e d from e q u a tio n 8 .
The chamber
d ia m e te r is c a l c u l a t e d from e q u a tio n 5:
Re
2V o
v A,
2V o
y Re
C
.
8W d
h
4
'
D=
w
The le n g th and d ia m e te r o f the chamber a re a r r i v e d a t through a t r i a l a n d - e r r o r pro c ed u re .
Reference ( 7 ) giv es a graph o f Re vs
= S t Pr2 /3
where
(
10)
T h is in c lu d e s Reynolds numbers i n both th e la m in a r and t u r b u l e n t - f l o w
r e g io n s .
fo u n d .
Thus, f o r a given Reynolds number, the Stanton number can be
Then L and D can be c a l c u l a t e d ,
re s p e c tiv e ly .
It
is assumed t h a t a i r is flo w in g through th e chamber:
Tn
9Z
= SlOO0F
Tn
9I
= 1700°F
Vf m
= 3 . 3 x 10~5 I b fflZ f t s e c
Pr
=
.72
Wg
=
1 .2 7 9 x IO6 I b / h r
■ pa v
d
o
using e q uations 8 and 9 ,
= -13 l b / f t 3
=0.25
inches
According to th e d a ta o f r e fe r e n c e
( 1 7 ) , a high Stanton number can be
reached in the la m in a r f lo w re g io n (Re < 2 0 0 0 ) .
is in v e r s e ly p ro p o rtio n a l
to Re, the r e s u l t i n g design has a very l a r g e
c r o s s - s e c t io n a l a r e a , and a small column h e i g h t .
param eters i n th e t u r b u l e n t re g io n a re used.
maximum
However, s in c e d ia m e te r
Thus,
design
In t h i s r e g i o n , a
o f 0 .0 0 3 8 occurs a t Re = 7000.
An average AT o f 155°F is taken from e s t a b l i s h e d d a ta f o r c o n v e c tiv e
h e a t t r a n s f e r from cored b r ic k s to a i r
(5).
I n c o r p o r a t in g t h i s data
i n t o e q u a tio n s 8 and 9 g iv e s :
A t Re = 7000, S t = .00 4 7 from e q u a tio n 10.
■-
69 -
. L = 2 3 .3 f t
D = 8 .9 f t
As a check, the chamber is s iz e d assuming t h a t h o t gas i s flo w in g
through th e chamber.
A g a in , e s t a b l i s h e d data ( 5 ) gives an average AT
between th e ho t gas and the cored b r i c k s o f IOO0 F.
The f o l l o w i n g
param eters are used:
T
= 3500°F
g2
Tn = 2300°F
9I
y AV = 3 . 5 x IO- 5 I b ^ / f t s e c
Pr
P
= .72
= .089 l b / f t 3
W
g
= 1 .3 0 4 x IO 6 l b / h r
m
d
= 0 .2 5 inches
o
F o llo w in g th e procedure o u t l i n e d above, the f o l l o w i n g d a ta are
developed:
L = 2 0 .0 f t
D = 8 .7 f t
Since th e chamber dimensions c a l c u l a t e d from a i r flo w d a ta a re l a r g e r ,
th e y a re c o nsidered c o n s e r v a t iv e and a re used in a l l
c a lc u la tio n s .
subsequent
- 70 CHAMBER PRESSURE DROP
Pressure drop is c a l c u l a t e d across th e chamber, h e i g h t .
The
momentum e q u a tio n f o r flo w in a c i r c u l a r pipe gives ( 1 6 ) :
where
- AR
_
4 w
4L
'
dO
(H )
, the w a ll shear s t r e s s , can be d e fin e d in terms o f the
t
Fanning f r i c t i o n f a c t o r ( 9 ) as:
Ub^Pf
"w -
(
29;
12)
S u b s t i t u t i n g e q u a tio n 12 i n t o e q u a tio n 11:
-
AP
AL
Now, s in c e Re
2db2 pf
d O9 C
V dO
we can w r i t e
Z f y 2 Re2
-AP
AL
(1 3 )
O r, o v e r th e o v e r a l l
chamber h e i g h t L,
-AP ==
(1 4 )
do V
The B la s iu s e q u a tio n ( 9 )
i s used to d e fin e th e Fanning f r i c t i o n f a c t o r
i n th e t u r b u l e n t flo w re g io n :
f .= 0 .0 7 9 Re"^
(15)
-7 1
-
Thus, using e quations 15 and 14 and employing the a i r f l o w data used
p r e v i o u s l y , th e chamber pressure drop i s :
-AP = 4 .4 3 psi
APPENDIX E:
I.
72 -
COST PREDICTION FOR FALLING-PARTICLE AIRE PREHEATER
Costs
In s u la tio n
U n it p r ic e s f o r r e f r a c t o r y i n s u l a t i o n m a t e r i a l
Appendix A - 6 .
In itia lly ,
a re p resented in
chamber volumes f o r each i n s u l a t i o n ty p e
a r e c a l c u l a t e d using
V = — J—
(D * - D* )L
.
(I)
See F ig u re 5 f o r column i n s u l a t i o n c r o s s - s e c t io n and d e s ig n a tio n
o f s p e c ific in s u la tio n
ty p e s .
Note:
assumed a t each end o f the column.
a re doubled.
Hem ispherical
caps a re
I n s u l a t i o n costs f o r ends
T h e . f o l l o w i n g data r e s u l t :
(One U n i t )
0 .0 3 8 i n . Blowout
0 .0 4 2 i n . Blowout
In s u la tio n
Body
1 .0 8 x IO4
7500
Volume ( F t ^ )
Ends
3200
2900
T o ta l
1 . 4 x IO4
1 .0 4 x IO4
TOTAL COST
2.
$ 1 .7 3 x IO6
$ 1 .3 3 x IO6
S te e l Column Cost
To c a l c u l a t e the necessary s t e e l
th ic k n e s s f o r th e column, the
f o l l o w i n g r e l a t i o n between p re ss u re and t e n s i l e s t r e n g t h is used:
2 TrdtL = 2 ttL pr
(2 )
-
73 -
where
r = column in s id e ra d iu s
t = s te el
th ic k n e s s
p = column i n t e r n a l
a = s te e l
pressure
t e n s i l e s tr e n g th
L = column h e i g h t
Thus, i t f o llo w s t h a t
(3 )
where D is th e column
o f a = 1 .x I p s i
d ia m e te r ( i n c l u d i n g i n s u l a t i o n ) .
is used f o r s t e e l .
Note:
caps a re assumed a t each end o f th e column.
a re doubled.
A value
A g a in , hem is p h e rica l
S te e l costs f o r ends
Using e q u a tio n 3 t o c a l c u l a t e the s t e e l
th ic kn es s
giv es th e f o l l o w i n g data (a s t e e l d e n s it y o f 490 lb / f t ^ is
assumed):
.
(One U n i t )
0 . 0 3 8 i n . Blowout
0 .0 4 2 i n . Blowout
S te e l
Body
4 . 3 7 x IO 5
Weight ( I b ffl)
Ends
1 .6 x IO 5
. 1 .4 x IO 5
T o ta l
5 .9 7 x IO 5
4 .3 3 x IO 5
$ 2 .2 7 x IO 6
$ 1 .7 2 x IO 6
TOTAL COST
2 .9 3 x IO 5
-
3.
74 -
Alumina P a r t i c l e Cost
In p r e d i c t i n g th e mass o f p a r t i c l e s
a i r p re h ea te r,
it
needed to i n i t i a l l y
charge the
i s assumed t h a t a p a r t i c l e bed a p p ro x im a te ly
4 f e e t deep w i l l . l i e above the top and m iddle d i s t r i b u t o r p la te s
eac h, and a t th e chamber bottom.
In a d d i t i o n ,
it
is assumed t h a t
the p a r t i c l e mass in th e pneumatic r e c y c le system w i l l
equal
about
the mass o f p a r t i c l e s above one d i s t r i b u t o r p l a t e .
In
p r e d i c t i n g how much o f the f a c t o r y - s u p p l i e d p a r t i c l e stock can be
used i n
each b lo w o u t, i t
is
assumed t h a t 81% o f the s to c k can be
used to
a ch ie v e a 0..038. i n :
b lo w o u t, and 54% o f th e s to c k can be
used to
a c h ie v e a 0 .0 4 2 i n .
b low out.
Using these f i g u r e s and
O
assuming a bed d e n s it y o f 135 l b ^ / f t , the f o l l o w i n g p a r t i c l e
masses are p r e d i c t e d . ( . a p a r t i c l e c o s t o f $ . 2 5 / l b m is assumed):
0 .0 3 8 i n . Blowout:
M = 4 . 7 x IO^ lb
m
Cost = $ 1 .2 x IO 5
0 .0 4 2 i n . Blowout:
M = 6 . 1 x IO5 I b m
m
Cost = $ 1 . 5 x IO5
These masses a re o f f a c t o r y - d e l i v e r e d p a r t i c l e s to c k .
4.
M is c e lla n e o u s C a p i t a l
Costs
(a )
P ip in g - a p ip in g c o s t o f $ 1 0 0 0 / f t i s assumed.
In a d d i t i o n , i t
assumed t h a t 300 f t o f p ip in g i s necessary f o r each u n i t .
This
is
- 75 gives a p ip in g c o s t o f $3 x 1 0 ^ / u n i t .
(b )
Valves - f o u r v a lv e s a r e p r e d i c t e d pe r u n i t , a t a c o s t o f
$ 3 4 ,0 0 0 /v a lv e .
(c )
T h is gives a v a lv e c o s t o f $ 1 .3 6 x 1 0 ^ / u n i t .
In s tr u m e n t a t io n - i t
is assumed t h a t in s tr u m e n t a t io n costs w i l l
a p p r o x im a te ly $3 x IO^ f o r th e o v e r a l l a i r p r e h e a t system.
be
This
f i g u r e is used f o r both blow out c ases, and f o r th e c o r e d - b r ic k
system.
(d )
Foundations and S t r u c t u r e - th e o v e r a l l
c a p i t a l c o s t f o r the
fo u n d a tio n s and s t r u c t u r e o f th e u n i t i s assumed t o be 90% o f
the column s t e e l
5.
,
cost.
E s tim a tio n o f Annual Maintenance Costs
~
■ The m ajor annual c o s t f o r the a i r p r e h e a t e r is p a r t i c l e replacem ent
due t o p a r t i c l e breakup and b lo w o u t.
A ccording to a n a l y s is done
by W. E. G e n e t t i , the tu r n o v e r tim e d u rin g which th e t o t a l
p a r t i c l e bed must be re p la c e d can be
ro u g h ly e s tim a te d a t . 100 days.
A t a p a r t i c l e c o s t o f $ .1 5 x 1 0 ^ / u n i t , the annual p a r t i c l e
replacem ent c o s t f o r t w o . u n i t s
is a p p r o x im a te ly $ 2 .1 x 1 0 * \
■: /• •
.
APPENDIX F :
I.
76 -
COST PREDICTION FOR CORED-BRICK A IR PREHEATER
I n s u l a t i o n Costs
An i n s u l a t i o n th ic k n e s s o f 3 . 5 f e e t is used f o r the c o r e d - b r ic k
columns, th e same as w i t h th e f a l l i n g - p a r t i c l e
F ig u r e 5 f o r i n s u l a t i o n c r o s s - s e c t i o n .
column.
See
A g a in , e q u a tio n I in
Appendix E - I i s used to c a l c u l a t e volumes f o r each i n s u l a t i o n
ty p e .
Note:
Hem ispherical caps a r e assumed a t each end of. the column,
and i n s u l a t i o n costs f o r the ends a re doubled.
(One U n i t )
I n s u l a t i o n . Volume, f t d
Cost
Body
3168
$ 3 . 1 8 x IO5
Ends
1763
3 .4 4 x IO 5
• 8098
$ 6 . 6 2 x IO 5
TOTAL
2.
S te e l
Column Cost
The r e l a t i o n s h i p used to c a l c u l a t e the thic k n e s s o f the s te e l
column f o r th e c o r e d - b r ic k a i r p r e h e a te r is the same as t h a t used
in
Appendix E - 2 . f o r th e f a l l i n g - p a r t i c l e a i r p r e h e a t e r .
Knowing
th e column t h i c k n e s s , t h e t o t a l mass o f s t e e l necessary f o r the
column can then be p r e d i c t e d .
Note:
A g a in , h e m is p h e ric a l s t e e l caps a re assumed a t each end o f
th e column.
S te e l
costs f o r th e ends a re doubled.
A s te el cost
- 77 o f $3/1 t>m is assumed.
(One U n i t )
Ps^e e -] = 490 I b mZ f t 3
S te e l Weight ( I b m)
Cost
Body
3 X IO4
Ends
2 . 1 x IO4
1 .2 6 x IO 5
TOTAL
5 .1 x IO4
2 . 1 6 x IO5
3.
9 x IO4
Cored B r ic k Costs
The cored b r i c k h e a t t r a n s f e r m a t e r i a l
Norton AH299.
The m a t e r i a l
has 0 . 2 5 inch cored holes g i v in g i t a
25% geom etric c r o s s - s e c t io n a l
p o ro s ity .
p o r o s i t y and a p u r i t y o f 99.5% a lu m in a .
$ 3 8 1 /b u lk ft .
It
used in t h i s a n a ly s is is
I t has an 18% m a t e r ia l
The m a t e r i a l
c o s t is .
is assumed t h a t th e column is c o m p le te ly
f i l l e d w ith cored b r i c k .
Volume = — f — . D2L = 1450 f t 3
Cost o f Cored B r ic k = $ 5 .5 2 x IO 3
4.
(a )
, M is ce llan e o u s C a p i t a l
Costs
P ip in g - a p ip in g c o s t o f $ 1 0 0 0 / f t is assumed.
A p i p i n g len g th
o f 1100 f e e t f o r the o v e r a l l s e v e n - u n i t a i r p r e h e a t complex is
assumed.
. (b )
This giv es a t o t a l
Valves - i t
p ip in g c o s t o f $ 1 .1 x 10®'.
i s assumed t h a t f o u r h ig h -t m p e r a tu r e v alv es a re needed
f o r each column.
''
V alve c o s t is $ 3 4 , 0 0 0 / v a l v e .
x-
,
•
:
x-- A .
T h is gives a
:
-x/ :- A . - / , - -
;
-
78 -
v a lv e c o s t o f $ 1 .3 6 x 1 0 ^ / u n i t .
(c )
In s tr u m e n t a t io n - as w it h th e f a l l i n g - p a r t i c l e
system,
it
is assumed t h a t o v e r a l l
th e c o r e d - b r ic k system w i l l
(d )
a i r p r e h e a te r
in s tr u m e n t a t io n c osts f o r
be a p p ro x im a te ly $3 x 10^.
Foundations and S t r u c t u r e - the o v e r a l l
c a p ita l
c o st f o r
fo u n d a tio n and s t r u c t u r e f o r th e c o r e d - b r ic k system i s e x t r a ­
p o la te d from c o s t data s u p p lie d by W. E. G e n e tti
f i r e d c o r e d - b r ic k a i r p r e h e a t system.
fo r a d ire c t-
This c o s t f o r th e o v e r a l l
i n d i r e c t - f i r e d system i s a p p r o x im a te ly $3 x 10®. 5
5.
E s t im a tio n o f Annual Maintenance Costs
Annual costs f o r th e c o r e d - b r ic k a i r p r e h e a te r a re m o s tly due
t o c o r e d - b r ic k re p la c em e n t due to therm al shock and h i g h r te m p e ratu re
c o rro s io n .
E stim ated annual costs f o r a system o f t h i s c a p a c ity
a r e found to be $ 1 . 4 x .10®.
a t % 1 .7 y e a r s .
The m a t r i x l i f e t i m e is e s tim a te d
T h is data is p re se n te d i n r e f e r e n c e ( 1 0 ) .
APPENDIX G:
I.
DESIGN DATA FOR COAL CARBONIZATION SYSTEM
Mass and Energy Balances
A ll
flo w r a t e s a re l a b e l e d on F ig u re d 6.
From r e f e r e n c e ( 1 0 ) ,
th e combustion a i r r a t e A 1 f o r the i n t e r m e d i a t e
BTU fu e l
gas is
-A' = 1 2 .4 7 G
Also from r e fe r e n c e ( 1 0 ) ,
fo llo w in g :
(I)
coal c a r b o n i z a t i o n y i e l d s th e
.
2000 I b ffl Coal
->
1400 I b m coke + ~ 600 lb f u e l
gas
Thus, using th e nom enclature o f F ig u re 6,
A
b
=
600
1400
*
K
(2 )
Now, to r e l a t e A and G, an energy ba lanc e is ta k e n .a c r o s s the
a i r . p r e h e a te r ( n e g l e c t i n g energy lo s s e s ) :
3500°F
(G + A 1) /
Cp
dT
exhaust
2330°F
3100°F
dT
A /
Cp
a ir
1700°F
(3 )
Using th e h e a t c a p a c i t y data from Appendix A i n e q u a tio n 3 , and
s u b s t i t u t i n g i n e q u a tio n s I and 2 , g iv e s :
K =; .1773 A
As an i n i t i a l
te s t,
it
(4 )
is.assum ed t h a t th e f u e l
MHD combustor is pure coke, d e l i v e r e d a t T c a rb o n ize r.
f lo w t o the
1800°F from th e coal
From th e re q u ire m e n t t h a t th e therm al
in p u t t o th e
MHD du c t be 400 MW, and n o tin g t h a t ^ c o m b u s tio n ~ 14»000 B TU/lbm
- 80 -
■and Cp - = .36 3 B T U /lb ^ °F f o r coke,
KAHcomb
+ KC
(1 8 0 0 °F - 7 7 °F ) = 1 .3 6 6 x IO9
m
which y i e l d s
’’
K = 9 . 3 4 x 10
(5 )
A
l b m/ h r .
Now, from r e f e r e n c e ( 1 0 ) , th e
a i r re q u ire m e n t f o r combustion o f coke is A = 1 1 . 2K.
an a i r f l o w r a t e o f A = 1 .0 4 6 x 10® I b fflZ h r .
This gives
S u b s titu tin g th is
v a lu e i n t o e q u a tio n 4 giv es th e coke pro d u c tio n r a t e necessary to
produce enough f u e l
gas to h e a t t h i s a i r flo w r a t e :
K = ( . 1 7 7 3 ) ( 1 . 0 4 6 x IO 6 ) = 1 .8 5 5 x IO 5 l b ffl/ h r
(6 )
As can be seen, th e coke f lo w r a t e from th e c a r b o n i z e r is n e a r ly
tw ic e th e coke f l o w r a t e to th e MHD combustor.
- 81 APPENDIX H :
I,-
DESIGN DATA FOR COAL. GASIFICATION SYSTEM
Mass and Energy Balances
Flow r a t e s a re l a b e l e d .o n F ig u re I .
From r e fe r e n c e ( 7 ) ,
the
c o n ve rs io n r a t e f o r th e .C O g -a c c e p to r g a s i f i c a t i o n process is
~ 60%.
Then,
-
,
G = .6 0 D
(I)
For th e combustion o f a high BTU g a s , t h e a i r r a t e necessary i s :
A' = 17.24G
.
Now, an energy balance across t h e a i r p r e h e a te r y i e l d s
(2 )
(n e g le c tin g
energy l o s s e s ) :
3400°F
3100°F
(G + A 1) /
CRexhaust
2330'
Note:
I
1700'
a ir
a fla m e te m p e ra tu re o f 3 4 0 0 °F is assumed f o r combustion o f
th e gas (1 0 )..
A ls o , th e h e at c a p a c it y o f th e combustion products
i s assumed to be c lo s e to t h a t o f th e i n t e r m e d i a t e - BTU gas
p re s e n te d in Appendix A - 3 .
Since ambient coal i s being used in
th e MHD combustor, A = 1 .2 7 9 x IO^ l b ^ / h r (see Appendix B - 2 ) .
S u b s t i t u t i n g e q u a tio n 2 i n t o e q u a tio n 3 and s o l v i n g f o r G g iv es :
G =
Using t h i s
8 .0 5 3 x IO 4 l b m/ h r
value i n e q u a tio n I giv es th e coal
(4 )
i n p u t r a t e to th e
- 82 g a s ifie r:
D = 1 .3 4 x IO 5 l b m/ h r
(5 )
S ince the coal f l o w r a t e to th e MHD duct i s 1 .5 2 7 x IO^ I b fflZhr
(see Appendix B - 2 ) , th e coal f lo w r a t e to th e g a s i f i e r is *4 7 % o f
the t o t a l
2.
coal r a t e to t h e power g e n e r a tin g complex.
■ C a p i t a l and Annual Cost P r e d i c t i o n
Reference ( 7 ) gives a c a p i t a l
c o s t o f $103 x IO^ f o r a COg -
a c c e p to r g a s i f i c a t i o n system w it h an o u tp u t o f 250 x 10° s c f
3
gasZday.
Assuming a, gas d e n s i t y o f . O S l l b fflZ f t
th e c a p i t a l
, an e s t im a te o f
c o s t o f t h e g a s i f i c a t i o n system f o r t h e a i r
p re h ea te r is :
C = (103 x IO 6 )
[■- 8 ---° -5- - y 1" —
1
x
-------- ^
------------ ]
2 5 0 x l0 b( . 0 5 1 )
= $ 2 7 .5 x IO 6
The annual o p e r a t in g c o s t o f the 250 x 10
as $16 x IO6 .
6
scfZday p l a n t is given
Thus, f o l l o w i n g th e same procedure as above, th e
annual o p e r a t in g c o s t o f t h e g a s i f i c a t i o n system f o r th e a i r
. p r e h e a te r can be e s tim a te d as:
Annual o p e r a t in g c o s t = $ 4 . 3 x I O6
•Vi.
'
BIBLIOGRAPHY
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S h i e n d l i n , A. E . , and Jackson, W. D. , "MHD E l e c t r i c a l Power
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.
'
- -t-
.
■
,
•• •
• • J' >
-
V.- '*"
i
■t- - . . ■ ■>.
•
r." ^ .
-,"f11•
•
• .
« * . ., r
• -X
4'S • t, '
'\
- '- V - ', V -
- •• •- -V."1-.-,-
- 84 ~
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MONTANA STATE UNIVERSITY LIBRARIES
1762 1001456 5 3
Ji+525
co p .2
Jen se n , Chris D
Design o f an i n d i r e c tf ir e d f a l l i n g - p a r t i c l e
a i r p re h e a te r f o r MHD
power g en eratio n
DATE
IS S U E D TO
-a .
J A N ^ n A*P s ,
-
i^ b ic \< .
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/
W^
5 8 1 -Z r.t
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^ iffQ lin i
h
/P '3 7 f
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