GAS PIPELINE HYDRAULICS. HYDRAULICS. E. SHASHI MENON. CAPÍTULO 1°. EJERCICIOS EJERCICIOS PROPUESTOS
1. A natural natural gas gas !"tur# $%ns!sts $%ns!sts %& t'r## t'r## $%(%n#nts) $%(%n#nts) C1) C1) C*) an+ C,. T'#!r %l# %l# &ra$t! &ra$t!%ns %ns an+ -!s$%s! -!s$%s!t!# t!#ss at a (art!$ (art!$ula ularr t#(#r t#(#ratu atur# r# ar# !n+!$a !n+!$at#+ t#+ #l%/0
C%(%n#n M%l# M! 2!s$%s!t345!6) t ra$t!%n Y! $P C1 8)988 1: 8)81,8 C* 8)8<8 ,8 8)811* C, 8)8*8 ;; 8)889< T%tal Cal$ulat# t'# -!s$%s!t3 %& t'# gas !"tur#. RTA/
μ=
Y!M! 17*
5!Y!M! 17*
,):88 8);,< 8)1,, ;)1=1
8)8;:< 8)88;9 8)881, 8)8>,8
La -!s$%s!+a+ (ara una #?$la +# gas#s #s)
M ) ∑ ( μ μ y √ M M ) ∑ ( y √ M i
i
i
i
i
Ent%n$#s) μ=
0,0530 cp 4,171
= 0,0127 cP
*. At 188 188 (s!g (s!g an+ =>° =>°) a gas 'as 'as a -%lu -%lu# # %& <88 <88 &t ,. I& t'# -%lu# !s @#(t $%nstant an+ t'# gas t#(#ratur# !n$r#as#s t% 188°) /'at !s t'# &!nal (r#ssur# %& t'# gas B##(!ng t'# (r#ssur# $%nstant at 188 (s!g) !& t'# t#(#ratur# !n$r#as#s t% 188°) /'at !s t'# &!nal -%lu# Us# 1;.=, (s! &%r as# (r#ssur#. RTA/
C%n+!$!%n#s !n!$!al#s0 P1 188 (s!g 1;)=, (s! 11;) =, (s!a
T1 =>;:8 >,> R C%n+!$!%n#s &!nal#s0 T* 188;:8 >:8 R
Da+% u# #l -%lu#n #s $%nstant#) t#n#%s P1 P2
T 1
=
T 2
P2=
Ent%n$#s)
114,73 ( psia ) ∗560 R 535 R
=120,09 psia
S! la (r#s!Fn s# ant!#n# $%nstant#) t#n#%s0 C%n+!$!%n#s !n!$!al#s 21 <88 &t, T1 >,>R C%n+!$!%n#s &!nal#s T* >:8R V 1 V 2
=
T 1 T 2
3
V 2=
800 ( ft )∗560 R 535 R
=837,38 ( ft 3)
,. Cal$ulat# t'# a((ar#nt %l#$ular /#!g't %& a natural gas !"tur# t'at 'as <9 #t'an#) < #t'an#) * (r%(an#) an+ 1 n%ral utan# as s'%/n #l%/. RTA/
n
M GAS=
M ∗Y ∑ = i
i
i 1
DFn+#0 M! #s la asa %lar +# $a+a $%(%n#nt# Y! la &ra$$!Fn %lar +# $a+a $%(%n#nt#
C%(%n#nt#
M%lar <9 < * 1 188
CH; C*H: C,H< C;H18 t%tal M GAS=18,1
Y!
M! 4l7l%l6
8)<9 8)8< 8)8* 8)81 1
1: ,8 ;; ><
M!Y! 4l7l %l6 1;)*; *);8 8)<< 8)>< 1<)1
Lb −m Lb− mol
;. Cal$ulat# t'# (s#u+%$r!t!$al t#(#ratur# an+ t'# (s#u+%$r!t!$al (r#ssur# %& a natural gas !"tur# $%ns!st!ng %& <9 #t'an#) < #t'an#) an+ , (r%(an#. T'# $r!t!$al (r%(#rt!#s %& C1) C*) an+ C, $%(%n#nts ar# as &%ll%/s0 RTA/
n
T pc =
n
Y ∗T P =∑ Y ∗ P ∑ = = i
i 1
C
pc
i
C
i 1
DFn+#0 T$ 3 P$ s%n la t#(#ratura 3 (r#s!Fn $rt!$as T($) P($) la t#(#ratura 3 (r#s!Fn (s#u+%$r!t!$as
Y! la &ra$$!Fn %lar C%(%n#n t CH; C*H: C,H< T%tal
M%lar
Y!
T$ 4 R 6
P$ 4Ps!a6
<9 < , 188
O)<9 8)8< 8)8, 1
,;, >>8 :::
::= =8< :1>
Y! T$ 4 R 6 Y! P$ 4Ps!a6 ,8>)*= >9,):, ;;)88 >:):; 19)9< 1<);> ,:9)*> ::<)=*
T pc =369,25 R P pc =668,72 Psia
>. I& t'# t#(#ratur# %& t'# gas !n t'# (r#-!%us #"a(l# !s <8° an+ t'# a-#rag# gas (r#ssur# !s 1888 (s!g) /'at ar# t'# (s#u+%r#+u$#+ t#(#ratur# an+ (s#u+%r#+u$#+ (r#ssur# %& t'!s gas Us# 1;.= (s!a &%r as# (r#ssur#. RTA/
Sa!#n+% u# (ara la #?$la +# gas#s t#n#%s) P pc =668,72 Psia T pc =369,25 R
T =80 ° F =540 R P=1000 psig + 14,4 psi a =1014,7 psia
Ent%n$#s) T T pr = = T pc
P pr=
540 R 369,25 R
=1,46
P 1014,7 PSIa = =1,52 P pc 668,67 PSIa
:. Cal$ulat# t'# gra-!t3 %& a natural gas !"tur# $%ns!st!ng %& <; #t'an#) 18 #t'an#) an+ : (r%(an#. r% t'# gas gra-!t3) $al$ulat# t'# (s#u+% $r!t!$al t#(#ratur# an+ (s#u+%$r!t!$al (r#ssur# &%r t'!s natural gas !"tur#. RTA/
C%(%n#nt#
M%lar <; 18 : 188
CH; C*H: C,H< t%tal G=
M GAS M AIR
=
19,08 29
Y!
M! 4l7l%l6
8)<; 8)18 8)8: 1
1: ,8 ;;
M!Y! 4l7l %l6 1,);; , *):; 19)8<
=0,66
Tpc =170.491+ 307.344 G =373.34 R Ppc= 709.604 – 58.718 G =670.85 psia
=. T'# (s#u+%$r!t!$al t#(#ratur# an+ (r#ssur# %& a natural gas !"tur# /#r# $al$ulat#+ as ,<8°R an+ :=> (s!a. I& t'# CO* $%nt#nt !s 1* an+ H*S !s **) $al$ulat# t'# a+ust#nt &a$t%r e an+ t'# a+ust#+ -alu#s %& t'# (s#u+%$r!t!$al t#(#ratur# an+ (s#u+%$r!t!$al (r#ssur#. RTA/
T pc =380 R P pc =675 psia COMPONENTS
%
CO2
12
H2S
22
=120 ( A − A 0,9
1,6
) + 15 ( ! −! ) 0,5
4
T " pc =T pc −
P" pc =
P pc∗T " pc T pc + ! ( 1− ! )
A 8)1* 8)** 8),; K 8)** =120 ( 0,34 −0,34 0,9
1,6
) + 15 ( 0,22 − 0,22 )= 31,1 R 0,5
4
T " pc =380 −31,1=348,9 R
P" pc =
675∗348,9 380 + 0,22 ( 1− 0,22 )∗31,1
=611,17 psia
<. Us!ng t'# Stan+!ngBat? $%(r#ss!!l!t3 $'art) $al$ulat# t'# $%(r#ss!!l!t3 &a$t%r &%r t'# gas !n Pr%l# = at <8° an+ 1888 (s!g. Us# t'# -alu#s %& Tpc an+ Ppc $al$ulat#+ !n Pr%l# =. RTA/
T =80 ° F =539.6 ° R T pc =367.38 ° R psia ¿ P pc= 648.9 [ psia ] |¿|=1000 + 14.7 =1014.7 ¿
P¿
P pr =
1014.7 [ psia ] P = =1.5637 P Pc 648.9 [ psia ]
T pr =
T 539.6 ° R = =1.4699 T Pc 367.38 ° R
9. A natural gas !"tur# $%ns!sts %& t'# &%ll%/!ng $%(%n#nts0
C%(%n# nt C1 C* C, N* CO* H*S
M%l# ra$t!%n Y! 8)<>8 8)88; 8)88* 8)81; 8)818 8)1*8
4a6 Cal$ulat# t'# a((ar#nt %l#$ular /#!g't %& t'# gas) gra-!t3) an+ t'# (s#u+%$r!t!$al) t#(#ratur# an+ (s#u+%$r!t!$al (r#ssur#. 46 Cal$ulat# t'# $%(r#ss!!l!t3 &a$t%r %& t'# gas at 188° an+ 1;88 (s!a. RTA/
C%(%n#nt
Y!
M!
T$4R6
P$4(s!a6
Y!T$ 4R6
C1 C* C, N* CO* H*S T%tal
8)<>8 8)88; 8)88* 8)81; 8)818 8)1*8
1* *; ,: *< ;; ,;
,;, >>8 ::: **=)8= >;=)>; :=1):=
::= =8< :1> ;91.: 18=1 1,8:
*91)>> *)* 1),,* ,)1=9 >);=> <8): ,<;),,:
n
T pc =
Y ∗T =384,336 R ∑ = i
C
i 1
n
Y ∗ P ∑ =
P pc =
i
=744,604 psia
C
i 1
G=
M GAS M AIR
= 15,278 =0,527 29
46 T =100 ° F =560,67 [ R ] P=1400 [ psia ]
Y!P$ 4(s!a6 >::)9> *)<,* 1)*, :)<<* 18)=1 1>: =;;):8;
Y!M! 18)* 8)89: 8)8= 8),9* 8);; ;)8< 1>)*=<
P pc =744,6 [ psia ] T pc=384,34 [ R ]
P pr=
P T 560,67 1400 = =1,88 T pr= = =1,459 P Pc 744,6 T Pc 384,34 # =0.81
18. T'# gra-!t3 %& a natural gas !"tur# !s 8.:*. Cal$ulat# t'# $%(r#ss!!l!t3 &a$t%r %& t'!s gas at 1;88 (s!g an+ a t#(#ratur# %& <8°) us!ng t'# CNGA #t'%+. T f =540 R Usando el método de la CNGA
# =
1
[( 1+
1
#
P a$g 344,400 ( 10 )
1,78 G
3,825
T f
)]
1,785∗0,62
=1 +
1400∗344 400∗(10)
# =0,821
3,825
540
=1,218
