EXPLOTACION DEL GAS NATURAL 1 ANALISIS DEL RESERVORIO RESERVORIO
Ejemplo 4.1.Se tiene una prueba isocronal y se esea conocer el potencial el reser!orio y el IPR para los "#toos si"pli$cao% &ones 'lount Gla(e y LIT) Datos: Pr = 1*+,,psi Tr = .,*/0 Tc = 2/0
Prof = 1+-**pies API = 2 S! = *%3
PM = 18,8305 SG = 0,742782152
Pr"e#a $soc $socro%al ro%al Per$& r$&'o'e("jo "jo
)*o+"e +"e
D"ra "rac$&% $&%
Pres res$&% $&%,P*.
Pres res$&%, $&%,P P*.
)a"'al 'al
)a"'al 'al
)a"'a "'al
Per$&'o
/o%'o
)a#e0a
as
)o%'e%sa'o
A!"a
)12 34
*r
ps$a
ps$a
55scf2 '
6PD
6PD
1. 13 13 .* .* .+ .+ 13
.+ 1. 1. 1. 1. -7
1*+,, ,71 3**2 +73 -2,7 3177
2*++ 2* +-7* --* .+3* +**
+%71, 3%.23 ,%--, 7%*7 3%.71
,. 77 27 1*2 72
3 11 1, 1, 1*
est4ti est4tica cainicial inici al 5u6o 1 5u6o. 5u6o5u6o+ 0lu6o 0l u6o e8tenio 8tenio
D$fere%c$al
Pse"'o
Pres$&%
Pote%c$al
D$fere%c$al
5,p.
Del 5,p.
,P89. 55PSI 89
1*2%,37 +7%32,-%32 73%*22 2-%2+,1%+,3 SU9ATORIA
DP892 7
Del
mps$a ps$a8 892 5mps$892 cp 5mps$892cp
1*%1*2 11%322 11%,- 11%3., 11%-7*
-3.-,13.3 1.*+ 2*+ 1323
1.7* .*., .++2 .,+2 12, 1*+3.
5,p.-#7!89
)a"'al
Del 5,p.2 7! 7!
7!89
as
mps$: ps$:92cp2 92cp2 5mscf
55scf2'89 f2'89
55scf2'
.3%,7 -.1%2---%, -+*%1, -11%31 1,-%.+
.-%.*-2%3+* -%7-. 3%.73 -2%+1 ..1%+1.
,. 11.+ 1..1.3. 1*2 +.*
+%71, 3%.23 ,%--, 7% 7%*7 3%.71 -.%711
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EXPLOTACION DEL GAS NATURAL . ANALISIS DEL RESERVORIO RESERVORIO
Método Simplificado.
Pr = 10 10477
Caudal de Gas MMscfd
Presión Fo Fondo Pf psia
Diferencial Presión!" Mmpsi!"
10477
0
7815
48,693304
4,817
6009
73,659448
6,296
4865
86,099304
7,377
3978
93,943045
8,08
6188
71,476185
6,281
Pr"e#a Isocro%al 5;to'o S$mpl$
1**)**
1*)**
D$fere%c$al 'e Pres$&% Ps$ 9
1)**
*)1* 1
1* )a"'al 'e !as ,55pc'
n=
log q1 − log q 4 log(Pr
2
− Pwf 21 ) − log(Pr 2 − Pwf 2 4 )
1**
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EXPLOTACION DEL GAS NATURAL ANALISIS DEL RESERVORIO RESERVORIO
Qg =C ( P Pr Pres$&% /o%'o Pf ps$a 1*+,, ,71 3**2 +73 -2,7 3177 *** .** 1*** *
D$fere%c$ al Pres$&%9 5mps$9 1*2%,3, .2 +7%32--* + ,-%32++ 7 73%*22-* + 2-%2+-*+ ,1%+,317 7+%,3,. 2 1*-%1, .2 1*7%,3, .2 1*2%,3, .2
2
Pwf
−
2
)
n
)a"'al 'e as 55scf'
)a"'al 'e as 55scf' IPR *
+%71,
+%71-77-3.
3%.23
3%33,+,*37
,%-,,
,%-7,23-1-
7%*7
7%*,+.+12-+
3%.71
3%11173*3 ,%++37,.3+ 7%,111,1+1 2%*311.37,, 2%1.33.,+,
Nos pone"os !alores arbitrarios para ar"ar nuestro IPR y eter"inar el AO0:2)1-99pc)
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EXPLOTACION DEL GAS NATURAL + ANALISIS DEL RESERVORIO RESERVORIO
IPR 1.*** 1**** 7*** Pf ps$
3*** +*** .*** * *
1
.
-
+
3
,
7! 55scf'
5;to'o 'e o%es 6lo"%t la0e Pr = 10477
Caudal de Gas MMscfd
Mmpsi"#MMscfd
48,693304
4,817
10,11
6009
73,659448
6,296
11,7
4865
86,099304
7,377
11,67
3978
93,943045
8,08
11,63
6188
71,476185
6,281
11,38
Presión Fon Fondo
Diferencial
Pf
Presión"
psia
Mmpsi"
10477
109,767529
7815
DP" # $
7
2
1* 1*
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EXPLOTACION DEL GAS NATURAL ANALISIS DEL RESERVORIO RESERVORIO
5;to'o 'e 6lo"%t la0e 1+)** 1.)**
;<8= : *)+,8 > 7)12 R? : *),
1*)** 7)** Dp27! ,Ps$9255pc' ,Ps$9255pc'
3)** +)** .)** *)** *
1
.
-
+
3
,
7
)a"'al 'e as ,55pc'
De acuero a los !alores obtenios por la @r4$ca y el a6uste lineal A : interseccin con e6e B
Aq + Bq 2 q
=
2
Pw f = Aq + Bq − Pwf
− A ±
Pres$&% /o%'o Pf ps$a 1*+,, 2+.2 7-7. 3.73 .-2
−
( PR 2 A 2
−
2 2
− Pwf
4 B ( PR 2
)=0 2
Pw f − Pwf
)
2 B
)a"'al 'e as 55scf' IPR * .%.-%2 3%.3 ,%*2
2
1*
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EXPLOTACION DEL GAS NATURAL 3 ANALISIS DEL RESERVORIO RESERVORIO
IPR 1* 2 7 , 3 Pf ps$a
+ . 1 * *
.***
+***
3***
7***
1****
1.***
7! 55scf'
Coe$ciente La"inar −
1424T A =
Coe$ciente Turbulencia
−
µ Z 0.472re + S ln
kh
B =
rw
3,161 X 10
−12
−
βγ g ZT
rwh 2
A: A>'
B
A´
A´/ A
AOF Tra s. (Mm scfd
0, 46520919
8, 3157
12, 43
1, 49421118
8, 834
Recome%'ac$&%: E8iste una peueFa turbulencia en el po(o) 5;to'o A%Bl$s$s L$t C4lculos aicionales para eter"inar la !iscosia y el ;actor H
P pc =706−51.7∗γ g−11.1∗γ g
2
P
=
Pr
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Temp. ,CR
Pres. ,Ps$ 0 2000 4000 6000 8000 10000 10477 •
730 730 730 730 730 730 730
555 555 555 555 555 555 555
Ppc ,Ps$a
Tpr
651,40625 651,40625 651,40625 651,40625 651,40625 651,40625 651,40625
1,31532 1, 1 ,31532 1, 1 ,31532 1, 1 ,31532 1,31532 1,31532 1,31532
Correlacin e 'rill an 'e@@s
Z = A +
1 − A
e
A *%.22+-3 + *%.22+-3 + *%.22+-3 + *%.22+-3 + *%.22+-3 + *%.22+-3 + *%.22+-3 + •
Tpc ,CR
B
+
D
C ∗ P Pr
6 * .%17*,7+ +2. 17%*,,.+ 1-+ 1+2%+.1, 1*1 ,21%7-22 , .2,-%27 23, -2.3%.-+ +,
) *%*2-21* +-2 *%*2-21* +-2 *%*2-21* +-2 *%*2-21* +-2 *%*2-21* +-2 *%*2-21* +-2 *%*2-21* +-2
D *%2,11, ,22 *%2,11, ,22 *%2,11, ,22 *%2,11, ,22 *%2,11, ,22 *%2,11, ,22 *%2,11, ,22
9#too e Lee% Gon(ales y Eain
1 *%72 *%7,. 1%*21 1%--3 1%7. 1%3+*
Ppr 0 3,07028 6,14056 9,21084 12,28112 15,35140 16,08367
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11 -. 1+ 1+7%327+ %*-72722 1%-2..*.* *%.+3 11 -. 1+
*%*,
Pse"'o Pote%c$al Pres$&% V$scos$'a'
/actor
Ps$a *
)p *
1
.***
*%*1,+
*%2--.
+***
*%*...
*%2,*.
3***
*%*.37
1%1*.2
7***
*%*-*
1%.,23
1****
*%*---
1%+,1.
1*+,,
*%*--2
1%17
P2"0
Del m,p
* 1.-1,*%-* 1 17,1+%+, 1+ .*.22.%3 .*+27.%*7 2, .*+112%.2 *3 .*-2+%.+
ps$2cp * .+3-+*31* %. 31,,32%1 ,,,+1+.+7 %2 712+2+7 %+ 717.*.,3* % 12++,2-1 %.
Pse"'o Pote%c$al +*** -** -*** .**
;<8= : *8J. > *)138
Del m,p Ac"m"la' o * .+3-+*31* %. 73+11*13%13+1.++1 . .+,+,-72 7 -.,3,33 7 -+,*13** 2
Del m,p Ac"m"la' o * .+3%-+*31 *. 73+%11*13 -13+1%.++ 1. .+,%+,-7 27 -.,%3,33 7 -+,*%13* *2
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M ( p ) =0.00002 p
2
+ 0.1617
p
A%al$s$s LIT 1****
1***
Del5,p-#7!89
1** 1**
1*
1 1
1* 7! 55scf'
1**
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Coeficiente %aminar & 'ur(ulento )*) & )+) Coeficiente Coefici ente %aminar %aminar * *, Mmpsi a!"#cp#M a!"#cp#MM Mscfd
164.3435929
Coeficiente 'ur(ulento + Mmpsia!"#cp#MM sia!"#cp#MMscfd
Potenci encia al tra tran nsien siente */F 'rans . Mms fd
Potenci encia al -sta sta(ili ilia ado */F -s t. Mms fd
9.56
9.49
22.77641183
Pres$&% /o%'o Pf ps$a 1*+,, ,71 3**2 +73 -2,7 3177 *
Pse"'o Pote%c$al 5mps$892 cp -3.-,13.3 1.*+ 2*+ 1323 *
)a"'al 'e as 55scf' IPR * +%,1. 3%+2-7 ,%-,,%2,3%-+ 2%3
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IPR 1.*** 1**** 7***
Pf Ps$
3*** +*** .*** * *
.
+
3 7! 55scf'
Ejemplo 4-1a.-
7
1*
1.
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1800 2000
0,016 0,0168
0,826 0,817
136198,547 145713,120
52 5 2227801 56382333
262915383 319297717
263 319
Pse"'o Pote%c$al 17* 17* 13* 13*
;<8= : *8J. *8
1+* 1+* 1.* 1.* 1** 1** 5,p 55ps$892cp
7* 3* +* .* * *
.**
+**
3**
7**
1*** 1.** 1+** 13**
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Mn Espesor Per;orao +7%** Mp Raio e po(o *%- R Raio e Drene 1***%* R * Porosia *%17 Per"eabilia el Gas 1%.@ Dano e 0or"acion 1,%** S Datos 'e Petro
pies pies pies "
pies pies pies
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703 × 10 −6
× k × h × (Pr (P r − Pfw ) Qg = = Mp cd re T × Z × µ × ln( ) − 0.75 + S rw − 703 × 10 × k × h C = re T × ln( ) − 0.75 + S rw 2
2
6
C
-%*-+E -% *-+E* *3 3 Pres$&% ps$ 1*+,, 2+.2 7-7. ,--+ 3.73 .-2 +121 -1+.*2 1*+7 *
V$scos$'a cp
*%*- *%*-*%*-. *%**%*.7 *%*. *%*.*%*. *%*17 *%*13 *%*1
1%+2 1%-2 1%.27 1%.*+ 1%113 1%*-7 *%2,7 *%2+. *%2-3 *%27 1
7! 55pc' calc"la'o * 1%-, .%72 +%,* 3%7. 2%3. 1.%++ 13%*7 17%2, .1%1 ..%.*
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Qg =
703 ×10 −6 × k × h × ( m( P )r − m( P ) fw ) re T × ln( ) − 0.75 + S rw
Pres$&% /o%'o Pf ps$a 1*+,, 2+.2 7-7. ,--+ 3.73 .-2 +121 -1+.*2 1*+7 *
Pse"'o Pote%c$al 5mps$892 cp -.1%-*1.%2 .-7%1 .*2%2 1373%7 1-11%1 237%1 37%. -71%+ 1-,%2 *
7! 55pc' calc"la' o IPR * 1%+ .%27 +%-. %, 3%,1 ,%, 7%32 2%1*%.3 1* 37
= Mpcd
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5;to'o Pse"'o Pote%c$al P ote%c$al 1.*** 1**** 7***
Pres$&% f ,ps$
3*** +*** .*** * *
.
+
3
7! 55pc'
7
1*
1.
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1048 0
0,016 0,015
0,958 1
0,0323663 0,0337853
5057,76844 4949,53853
5;to'o 'e 6lo"%t la0e 1.*** 1**** 7*** Pres$&% f
3***
19,14 19,56