Gas Lift Well Application Note - Wireless Data Acquisition and
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Gas Lift Workshop 1
Computer API Gas-Lift Design Course
Using Excel SpreadSheets
API RP 11V6:Recommended Practice for Design of
Continuous Flow Gas Lift Installations ----Using Injection Pressure Operated Valves
By Joe Dunn Clegg
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Gas Lift Workshop 2
Gas Lift Design ProgramsPETROLEUMTOOLBOX
Primary Programs AGL-DSN
AGL-GRAD
AGL-TEMP
AGL-SPACe
AGL-SET AGL-FLD
Secondary Programs COMPRESSOR
CT-TEMP
Vogel_IPR
Fet_IPR
Perm.Avg. Perm.Series
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Gas Lift Workshop 3
ADVANTAGES
Simple & Accurate Design No Black Box (all formulas accessible)
Economical ($495) Easy Printout of Data
Convenient to Alter Data For Both Injection Pressure and
Production Pressure Operated Valves
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Gas Lift Workshop 4
Best Suited For 2-3/8, 2-7/8 & 3.5 OD Tubing
Moderate Rates
API Design Procedures
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Gas Lift Workshop 5
15-Nov-97 VOGEL OIL IPR: WITH SKIN CORRECTION
WELL NAME: API Problem No. 1 v:Vogel Factor (Opt) 0.2 ---
PS:STATIC RES. PRESSURE 2,125 PSIA S:SKIN 0.00 'BASE
PB:BUBBLE POINT PRESSUR 2,125 PSIA Re:EXTERNAL 660.0 feetPF:FLOWING BH PRESSURE 1,941 PSIA Rw:WELLBORE 0.35 feet
QF:PRODUCTION RATE 200.0 BPD
PRESSURE NO SKIN BASE W/SKIN IPR_VOG
2125.0 PSIA 0 BPD 0 BPD VERSION 5.12125.0 PSIA 0.0 BPD 0.0 BPD (C) COPYRIGHT
1912.5 PSIA 229.5 BPD 229.5 BPD 1997.0
1700.0 PSIA 437.7 BPD 437.7 BPD Clegg & Boone
1487.5 PSIA 624.6 BPD 624.6 BPD ALL RIGHTS
1275.0 PSIA 790.1 BPD 790.1 BPD RESERVED1062.5 PSIA 934.2 BPD 934.2 BPD
850.0 PSIA 1057.0 BPD 1057.0 BPD
637.5 PSIA 1158.4 BPD 1158.4 BPD
425.0 PSIA 1238.5 BPD 1238.5 BPD
212.5 PSIA 1297.2 BPD 1297.2 BPD
0.0 PSIA 1334.6 BPD 1334.6 BPD
INPUT ANY NEW PWF 1200.0 PSIA new Qf= 843.4 BPD PI @ Qf= 0.91
Ql/Qmax = 1.0 - v*(Pwf/Pr) - (1-v)*(Pwf/Pr)^2
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IPR_VOG: VOGEL OIL W ELL IPR
0
500
1000
1500
2000
2500
0 500 1000 1500 2000
PRODUCTION RATE (BPD) OR (M^3/D)
PW
F;FLOW
INGP
RE
SSURE
(PSIA)O
R(
kPa)
NO SKIN WITH SKIN
API Problem # 1
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Outflow: Multiphase Vertical Flow
Empirical Models
Gilbert (CA oil wells)-developed 1940 to1950 but published in 1954
Poettmann & Carpenter (no slip) -1952
Baxendell & Thomas (high rate extension of P&C)-1961
Duns & Ros (lab data)-1961
Ros & Gray (improved D&R)-1964
Hagedorn & Brown (most used--slip?)-1964
Orkiszewski (Exxon composite)-1967
Beggs & Brill (incline flow)--1973
MMSM ( Moreland-Mobil-Shell-Method)-1976
Mechanistic Models $
Aziz, Grover & Fogarasi-1972
OLGA Norwegian- 1986
Ansari. Et al. 1990
Choksi, Schmidt & Doty-1996 Brill, et al
Shell : Zabaras-1990Others
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.
0 1 2 3 4 5
1
2
3
4
5
Thousands
Thous
ands
RATE(BFPD)
Pwf:BHFlo
wingTub
ingPress
ure(PSIG)
1.995"
2.441"
2.992"
3.467"
3.958"
TUBINGPERFORMANCE (OUTFLOW) CURVESFOR10,000 FT WELL W/ 1000 GLR& 50%CUT
Typical Tubing Outflow Curves
Rate in 1000 BFPD
PwfPwf
in1000psi
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PrPwf
o
E.C.
Upper Gradient Curves (Trace)
Lower Gradient Curves(0.42 psi/ft above BP)
200
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Depth
(ft)
Pressure (psig)
14001000600
x400 bpdx500 bpd
x600 bpd
x700 bpd
Gas Injection Pressures
Equilibrium Curve
Benefit from Higher Gas Injection Pressure
0
.
Dw
x 200 bpd
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Problem: API RP 11V6 Exp. No. 1
Q=Production-maxDw=Depth--8000
Pws=BHP 2125 psig
Test: 200 BFPDw/ Pwf = 1941 psig
RGO=GOR--700Water Cut --50 %
Oil Gravity 35 API
Water SG 1.07
Gas Gravity--.65
PD = 25 psi **Min Spacing = 250
Csg Size -- 7 OD
Tbg Size--2.875OD
Pwh = 100 psig
Pg=Inj gas--1200 psigQi=Inj --
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15-Nov-97 GAS LIFT DESIGN PROGRAM
-----------INPUT DATA---
WELL NAME: API Example No. 1
1 Pwh: WELLHEAD 100 psi AGL_DSN VERSION 5.02 Pg:INJ GAS PRES 1200 psi (C) COPYRIGHT 1992-96
3 SGi: SG .of Ig 0.650 air=1 BY DOUGLAS M. BOONE
4 Tgs:Ig TEMP @ SURF 78 'F AND JOE DUNN CLEGG
5 Tf:TEMP OF FORM 178 'F ALL RIGHTS RESERVED6 Dw: DEPTH: TVD 8000 ft
7 Tbg: TUBING ID 2.441 in --CALCULATIONS--
8 Pr:FORM PRES 2125 psi GAS Wt. 0.033 psi/ft9 Pb:BUBBLE POINT 2125 psi INJ PRESS @ TD 1464 psi
10 Pwf: FLOW BHP 1941 psi Qmax:MAX RATE 1335 bfpd
11 Ql: TOTAL FLOW 200 bfpd CHECKS--
12 Gfb: LOW GRAD 0.40 psi/ft Pr: ok13 Gff:UPPER GRAD ADJ 1.00 Pb: ok
14 START: INITIAL 400 bfpd Pwf: ok
15 INC:INCREASE RATE 50 bfpd
16 UNIT SELECTION E E or M (OILFIELD = E; METRIC = M)
8
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API Example No. 1 LIFT
FLUID INJ. TBG CSG DEPTH
RATE Pwf LEVEL GFA DEPTH PRES. Pgd OK
bfpd psi ft psi/ft ft psi psi
---------- -------- ------- ------ ------- -------- -------- ---
0 0 0 0.080 0 100 1200
1 400 1740 3650 0.106 5305 662 1375 OK2 450 1687 3783 0.109 5549 706 1383 OK
3 500 1632 3920 0.113 5802 753 1392 OK
4 550 1575 4062 0.116 6068 802 1401 OK
5 600 1517 4208 0.119 6346 855 1410 OK6 650 1457 4359 0.122 6637 911 1419 OK
7 700 1394 4515 0.126 6943 971 1429 OK
8 750 1329 4677 0.129 7266 1036 1440 OK
9 800 1261 4847 0.132 7607 1104 1451 OK10 850 1190 5024 0.135 7968 1178 1463 OK
8000 1464
PRESS [Ctrl"][C] TO VIEW EQUILIBRIUM CURVE CHART
Alter by changing Gff
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Gas Lift Workshop 14
AGL_DSN: EQUILIBRIUM PROGRAM
0
500
1000
1500
0 1000 2000 3000 4000 5000 6000 7000 8000
DEPTH (ft) or (meters)
PR
ESSURE(psi)
or(ba
r)
NEEDED INJ PRESSURE GAS INJ PRESSURE INJ GAS-SF
400 BFPD
850 BFPD
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Gas Lift Workshop 15
***GRADIENT CURVE FOR TWO-PHASE FLOW*** 15-Nov-97
***TYPICAL GRADIENTS FOR 50 % CUT WELLS***
WELL NAME: API Example No. 1
--INPUT DATA--- 1 Ql:TOTAL PROD RA 800.0 bfpd 800 Increments of 100 bfpd
100 to 1000 bfpd & 1500 & 2000
2 TBG: TBG ID 2.441 in OK STANDARD API SIZES
For 1.995,2.441,& 2.992 inches
3 CUT:Water cut ratio 0.50 b/b OK
(BASE CASE 0.50,OK IF CUT >0.35)
4 Pwh:Wellhead pres 100.0 psi OK RANGE 25 TO 499 PSIBase case for 100 psig
5 UNIT SELECTION E E or M (OILFIELD = E; METRIC = M)
Base on Modified Ros-Duns Correlation's
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Gas Lift Workshop 16
AGL_GRAD: GAS LIFT GRADIENT CURVES
0500
1000
15002000250030003500
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 1000
0
DEPTH (ft) or (meters)
PRESSURE
(psi)or(ba
r)
GLR=250(44.5) 500(89) 750(134)
1000(178) 1250(223) 1500(267)
GLR = 0
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Gas Lift Workshop 17
.
0 1 2 3 4 5
500
1000
1500
2000
2500
Thousands
Total Gas (Formation+Injection) in MCFD
Pt:Tub
ingPress
ure@
500
0ftinPSIG
Gas Lift Performance
For 2.992"Tbg & 2000 BPD
Excessive Gas
Opti-
mumGas
@ 5000
Max Rate
Excessive Gas
Insufficient
Gas
MMCFD
660
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Gas Lift Workshop 18
Choke Chart660
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Gas Lift Workshop 19
15-Nov-97 **PREDICTING TEMPERATURE PROFILES** (C) COPYRIGHT 92 &
WELL NAME: API Example No. 1 VERSION 5.0
--INPUT DATA--- --CALCULATIONS-- 1 Pwh: Wellhead Pressure 100.0 psi Tg:TEMP GRAD 1.250 'F/100'
2 Ts:Surface Temp 78.0 'F Cpl:SPEC. HEAT 0.743 BTU/lbm
3 Tf:Temp of Formation 178.0 'F f:DIM.TIME 2.306 't
4 Qo:Oil Rate 425.0 bopd SGo: OIL wt. 0.850 sp.gr.5 Qw:Water Rate 425.0 bwpd Wt1:MASS FLOW 3.48 lbm/sec
6 Qg:Form. Gas Rate 298.0 mcfd Wt2:MASS FLOW 3.78 lbm/sec
7 API: Oil Weight 35.000 'API U1:HEAT t.c. 111.67
8 SGw: SG. Water 1.070 sp.gr. U2:HEAT t.c. 6.30
9 SGg: SG Gas (Air = 1) 0.650 air=1 A1: COEF. 1.80E-04
10 TBG: Tubing OD 2.875 in A2: COEf. 9.53E-06
11 CSG: Casing OD 7.000 in SGM1:CORRECTION -0.003
12 Dw: Total Well Depth 8,000 ft SGM2:CORRECTION -0.004
13 Di: Depth of Gas Inj. 7,950 ft Flowing Twh = 131 'F
14 Qi:Gas Lift Inj. Rate 527 mcfd
15 UNIT SELECTION E E or M (OILFIELD = E; METRIC = M)
Based on paper by Sagar, Doty & Schmidt
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Gas Lift Workshop 20
AGL_TEMP: FLOWING TEMPERATURE PROFILE
0
50
100
150
200
250300
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
DEPTH (ft) or (meters)
TEMPERA
TURE
('F)of('C)
STATIC TEMP FLOW TEMP
131 F
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Gas Lift Workshop 21
SGi
Tgs Twh
InjectionPressureValve
Worksheet
Psep
100
25
15 Nov 97 ***GAS LIFT SPACING DESIGN***
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Gas Lift Workshop 22
15-Nov-97 GAS LIFT SPACING DESIGN
WELL NAME: API EXAMPLE No. 1
--INPUT DATA---
1 Psep: MIN SURF PRES. 100 psi AGL_SPAC VERSION 5.02 Pwh: WELLHEAD PRES 100 psi (C) Copyright 1995
3 Pg:INJ. GAS PRES. 1200 psi BY DOUGLAS M BOONE
4 Gs: FLUID GRAD. 0.465 psi/ft AND JOE DUNN CLEGG
5 Tgs:Ig TEMP @ SURF. 78 'F ALL RIGHTS RESERVED6 Twh: FLOW TEMP WEL 131 'F
7 Tf:TEMP FORM. 178 'F
8 SGi: INJ GAS (AIR=1) 0.650
9 DI1: LIFT DEPTH 1 4000 ft10 PI1: LIFT PRES 1 544 psi
11 DI2: LIFT DEPTH 2 8000 ft
12 PI2; LIFT PRES 2 1221 psi Pgd:MAX Ig PRES 1464 psi
13 Dw: MAX TVD 8000 ft Gg:INJ GAS GRAD 0.033 psi/ft14 Dmin:MIN SPACE 250 ft
15 PD: PRESSURE DROP 25 psi
16 UNIT SELECTION E E or M (OILFIELD = E; METRIC = M)
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Gas Lift Workshop 23
API EXAMPLE No. 1 Ppd(n) Pul(n) Pgd(n)
TBG PRE UNLOAD MAX CSG
***VALVE/MANDREL DEPTH*** psi psi psi------------------------- ------- ---------- --------- -------
SURFACE 0 100 1200 1200
DEPTH VALVE # 1 2497 ft 350 1261 1282
DEPTH VALVE # 2 4548 ft 623 1304 1350DEPTH VALVE # 3 6066 ft 865 1329 1400
DEPTH VALVE # 4 7083 ft 1045 1337 1434
DEPTH VALVE # 5 7702 ft 1162 1333 1454
DEPTH VALVE # 6 8000 ft 1221 1301 1464DEPTH VALVE # 7 #N/A ft 1221 #N/A #N/A
DEPTH VALVE # 8 #N/A ft 1221 #N/A #N/A
DEPTH VALVE # 9 #N/A ft 1221 #N/A #N/A
DEPTH VALVE # 10 #N/A ft 1221 #N/A #N/ADEPTH VALVE # 11 #N/A ft 1221 #N/A #N/A
DEPTH VALVE # 12 #N/A ft 1221 #N/A #N/A
TVD: MAX VALVE DEPT 8000 ft 1221 1464
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Gas Lift Workshop 24
AGL_SPAC: GAS LIFT SPACING
0
500
1000
1500
2000
0 1000 2000 3000 4000 5000 6000 7000 8000
DEPTH (ft) or (meters)
P
RESSURE(p
si)or(bar)
GAS INJ TBG SPACING
F 3/16 i h t
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Gas Lift Workshop 25
WELL NAME: Example Pvcd(n)D(n) Ppd(n) Pio(n) Piod(n) Tv CT Pvo(n) Qgi Pvc(n) V close
NO. DEPTH TBG PRES SURF V open @ VALVE TEMP T-R INJ GAS Surf close @ depth
ft psi psi psi 'F - psi mscfd psi psi
(INPUT) ------- ------- ------- ------- ------- ------- ------- -------- -------
0 100 1200 1200 131 - -
1 2497 350 1200 1279 146 0.836 1100 896 1109 1192
2 4548 623 1175 1318 158 0.817 1130 915 1103 1253
3 6066 865 1150 1339 167 0.803 1148 903 1094 1295
4 7083 1045 1125 1343 173 0.794 1153 798 1081 1315
5 7702 1162 1100 1333 176 0.789 1147 642 1062 1317
6 8000 1221 1075 1312 178 0.787 1132 483 1039 1303
7 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
8 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
9 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
10 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
11 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A12 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A
Dw 8000 1221.0 0.0 #N/A 178 0.000 0
X
X Install 1/4 screened orifice @ 7950
API Example No. 1 AGL_SET PROGRAM
For 3/16 inch port
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Gas Lift Workshop 26
AGL_SET:INJECTION PRESSURE VALVE DESIGN
Example
0
500
1000
1500
2000
0 1000 2000 3000 4000 5000 6000 7000 8000
DEPTH (ft) of (meters)
PRES
SURE(psi)or(bar)
INJ GAS TBG Temp VALVE SPACING
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Gas Lift Workshop 27
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Gas Lift Workshop 28
How about a production pressure
design for same well?
Pseudo surface Pressure =
100+.2(1200-100) = 320 psi
D2 = 8000 & P2 = 1221 psi as before
D1=4000 & P1 = 760 psi (straight line)
Use program AGL_SPACe
No valve pressure drop. PD = 0 psi
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Gas Lift Workshop 29
Psep
SGi
Twh
Worksheet
15-Nov-97 ***GAS LIFT SPACING DESIGN***
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Gas Lift Workshop 30
WELL NAME: API EXAMPLE No. 1 (Production Pressure Valves)
--INPUT DATA---
1 Psep: MIN SURF PRES. 100 psi AGL_SPAC VERSION 5.0
2 Pwh: WELLHEAD PRES 320 psi (C) Copyright 19953 Pg:INJ. GAS PRES. 1200 psi BY DOUGLAS M BOONE
4 Gs: FLUID GRAD. 0.465 psi/ft AND JOE DUNN CLEGG
5 Tgs:Ig TEMP @ SURF. 78 'F ALL RIGHTS RESERVED
6 Twh: FLOW TEMP WEL 131 'F7 Tf:TEMP FORM. 178 'F
8 SGi: INJ GAS (AIR=1) 0.650
9 DI1: LIFT DEPTH 1 4000 ft
10 PI1: LIFT PRES 1 760 psi11 DI2: LIFT DEPTH 2 8000 ft
12 PI2; LIFT PRES 2 1221 psi Pgd:MAX Ig PRES 1464 psi
13 Dw: MAX TVD 8000 ft Gg:INJ GAS GRAD 0.033 psi/ft
14 Dmin:MIN SPACE 250 ft
15 PD: PRESSURE DROP 0 psi
16 UNIT SELECTION E E or M (OILFIELD = E; METRIC = M)
x*
x
x
* Some designers drop the Ing. Gas pressure 100 psi
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Gas Lift Workshop 31
AP I E X AM PL E N o . 1 (P ro d u ctio n P ressu re P pd (n ) P ul(n ) P gd (n )
T B G P R E U N L OAD M AX C S G
***V AL V E /M AN D R E L D E P T H *** p s i p s i p s i------------------------- ------- ---------- --------- -------
S U R F AC E 0 320 1200 1200
D E P T H V AL V E # 1 2497 ft 592 1261 1282
D E P T H V AL V E # 2 4045 ft 765 1312 1334
D E P T H V AL V E # 3 5311 ft 909 1354 1376D E P T H V AL V E # 4 6342 ft 1027 1388 1410
D E P T H V AL V E # 5 7176 ft 1124 1416 1437
D E P T H V AL V E # 6 7851 ft 1203 1438 1459
D E P T H V AL V E # 7 8000 ft 1221 1273 1464
D E P T H V AL V E # 8 #N /A ft 1221 #N /A #N /A
D E P T H V AL V E # 9 #N /A ft 1221 #N /A #N /A
D E P T H V AL V E # 10 #N /A ft 1221 #N /A #N /A
D E P T H V AL V E # 11 #N /A ft 1221 #N /A #N /A
D E P T H V AL V E # 12 #N /A ft 1221 #N /A #N /AT V D : M AX V AL V E D E P T 8000 ft 1221 1464
Note: One additional valve required
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Gas Lift Workshop 32
AGL_SPAC: GAS LIFT SPACING
0
500
1000
1500
2000
0 1000 2000 3000 4000 5000 6000 7000 8000
DEPTH (ft) or (meters)
P
RESSURE(p
si)or(bar)
GAS INJ TBG SPACING
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Gas Lift Workshop 33
15-Nov-97 --PROGRAM TO SET SPRING LOADED FLUID VALVES--
WELL NAME: Variable Gradient Design for Fluid Valves
--INPUT DATA---1 Psep: MIN SURF PRES. 100 psi AGL_FLD VERSION 5.0
2 Pwh: WELLHEAD PRES. 320 psi (C) COPYRIGHT 1992 & 96
3 Pg:DESIGN INJ. PRES. 1200 psi BY DOUGLAS M BOONE
4 Gs:FLUID GRADIENT 0.465 psi/ft AND JOE DUNN CLEGG5 Tgs:Ig TEMP @ SURF 78 'F ALL RIGHTS RESERVED
6 Twh:FLOW TEMP 131 'F
7 Tf:TEMP OF FORM 178 'F
8 SGi: SG. INJ GAS 0.650 air=19 DI1: LIFT DEPTH 1 4000 ft --CALCULATIONS--
10 PI1: LIFT PRES 1 660 psi INJ GAS @ TD 1464
11 DI2: LIFT DEPTH 2 8000 ft 0.104 GL VALVE PPEF RA
12 PI2: LIFT PRES 2 1221 psi 0.0330 GAS WT. psi/ft13 Dw: MAX VALVE TVD 8000 ft
14 PORT/CHOKE: (1/64) 12 in
15 Av/Ab:VALVE P/B RATIO 0.094 mfg Press [Ctrl][a] for valve data
16 UNIT SELECTION E E or M
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Gas Lift Workshop 34
Variable Gradient Design for Fluid Valves
D(n) Ppd(n) Pgd(n) Piod @ Tv Qgi Pvo(n)
DEPTH TBG PRES PRES DEPTH @ VALVE INJ GAS TRO
ft psi psi psi 'F MSCFD psi------- ------- ------- ------- ------- ------- -------
0 0 320 1200 1300 131
1 2497 601 1282 1382 146 969 745
2 4045 776 1334 1434 155 997 9243 5311 918 1376 1476 162 1008 1071
4 6342 1034 1410 1510 168 993 1191
5 7176 1128 1437 1537 173 965 1288
6 7851 1204 1459 1559 177 931 1366
7 8000 1221 1464 1564 178 923 1383
8 #N/A #N/A #N/A #N/A #N/A #N/A #N/A
9 #N/A #N/A #N/A #N/A #N/A #N/A #N/A
10 #N/A #N/A #N/A #N/A #N/A #N/A #N/A
11 #N/A #N/A #N/A #N/A #N/A #N/A #N/A12 #N/A #N/A #N/A #N/A #N/A #N/A #N/A
Dw 8000 1464.4 178
X
X 12/64 Screened Orifice @ 7950
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Gas Lift Workshop 35
16-Nov-97 ARTIFICIAL LIFT SELECTION # BEFORE TAX COPYRIGHT(C) 1992-9 vERSION 5.
CONSTANT MAX LIFT RATE CLEGG & BOONE: ALL RIGHTS RESNAME: API Example DISCOUNT RATE 10.00 %
INSTALLATION $500,000 $ OIL PRICE INC/YR 1.00 %
MAX LIFT RATE 850 bpd INFLATION 3.00 %
INITIAL GAS GOR 700 ft 3/b LIFT EFF 25.00 %INITIAL H2O CUT 50.00 % LIFT DEPTH 8000 ft
END OIL RATE 20.0 bopd ENERGY COST 0.00 $/k-W-hr
END GAS GOR 700 ft 3/b --CALCULATIONS--
FLAT LIFE 0.00 yrs INITIAL OIL RATE 425 bbl
EFF DECLINE RATE 13.70 %/yr a:NOMINAL DECLINE 14.73 %/YR
OIL VALUE $20.00 $/bbl Qf:RESERVES FLAT 0 bbl
GAS VALUE $3.00 $/mcf Qec: RESERVES DEC 1,003,288 bbl
ROYALTY 25.00 % Qt:TOTAL RESERVES 1,003,288 bbl
DIR.OP (FIXED) $500.00 $/mo Td: TIME DECLINE 20.7 YRS
DIR OP(PER BFPD) $0.20 $/bbl Tt:TIME TOTAL 20.7 YRS
PULL & REPAIR $200 $/mo MAX PVP INCOME $9,691,467
(C) Copyright
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Gas Lift Workshop 36
ARTIFICIAL LIFT FULL CYCLE ANALYSIS
TYPICAL HIGH RATE EXAMPLE
($2,000,000)
$0
$2,000,000
$4,000,000$6,000,000
$8,000,000$10,000,000
0 5 10 15 20 25
LIFE (YRS)
CUMU
LATIVEPVP
IN
COME
($)
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The Winner
SpreadSheets$ $
?WG