Inverted ESP Sizing for a Downhole Water Sink

Spreadsheet

208 rows x 8 columns

Download
fx
A B C D E F G H
1 Inverted ESP Sizing — Downhole Water Sink
2 Blue cells on yellow are inputs. The pump curve is EXAMPLE data: replace it with the vendor's single-stage curve.
3
4 Loop Hydraulics Pump Curve — one stage at catalog frequency, water (EXAMPLE)
5 Target water rate (drainage = injection) 3000 bbl/d Rate (bbl/d) Head (ft/stage) BHP (HP/stage) Efficiency
6 Target sink at the drainage perforations (0 = design by rate) 0 psi 0 52 0.8 0
7 Water specific gravity (not the psi/ft gradient) 1.07 — 500 52.2 0.924 0.2072182846
8 Drainage zone static pressure 3200 psi 1000 51.5 1.003 0.3766741649
9 Drainage productivity index 10 bbl/d/psi 1500 50 1.081 0.5089734254
10 Injection zone static pressure (0 = same aquifer) 3246 psi 2000 47.6 1.159 0.6025776932
11 Injectivity index (end-of-life value) 8 bbl/d/psi 2500 44.4 1.234 0.6598836336
12 Vertical distance, drainage to injection perforations 100 ft 3000 40.3 1.308 0.6780755657
13 Flow-path ID, pump discharge to injection perforations 3.958 in 3500 35.4 1.378 0.6596014883
14 Flow-path length 150 ft 4000 29.6 1.441 0.6027639353
15 Known TDH at the design rate (0 = loop hydraulics) 0 ft 4500 23 1.491 0.5092396892
16 5000 15.5 1.509 0.3767662571
17 Pump, Drive and Motor 5500 7.2 1.397 0.2079497094
18 Catalog curve frequency 60 Hz
19 Design frequency (0 = solve for the design rate) 0 Hz
20 Stages installed (0 = minimum at catalog frequency) 0 stages
21 Recommended range, minimum rate 2200 bbl/d
22 Recommended range, maximum rate 3800 bbl/d
23 Motor nameplate power at catalog frequency 60 HP
24 Motor sizing safety factor 1.1 —
25 Motor OD 5.62 in
26 Casing (or shroud) ID at the motor 6.276 in
27 Water temperature at the motor 180 degF
28 Pump shaft diameter 0.875 in
29 Packer differential pressure rating 5000 psi
30
31 Loop Hydraulics at the Design Rate
32 Design basis Target rate
33 Design water rate 3000 bbl/d
34 Drainage sink: drawdown (Q / PI) 300 psi
35 Injection pressure build-up (Q / II) 375 psi
36 Water pressure gradient (0.433 × SG) 0.4632034632 psi/ft
37 Injection zone static pressure used 3246 psi
38 SG check OK
39 Same-aquifer check OK
40 TDH at the Design Rate, in Feet of Water
41 Sink head (drainage drawdown) 647.6635514 ft
42 Injection head (build-up) 809.5794393 ft
43 Static head between zones -0.691588785 ft
44 Flow-path friction 1.0814132 ft
45 TDH from loop hydraulics (sum of the four above) 1457.632815 ft
46 Design TDH (the known TDH when one is set) 1457.632815 ft
47 Share of the rate-driven head that makes the sink 0.4444444444
48 The pump pays for both ends of the loop: with II close to PI the design TDH is about twice the sink head.
49
50 Pump Sizing at Catalog Frequency
51 Best efficiency point (BEP) rate 2997.5 bbl/d
52 Efficiency at BEP 0.6780764853
53 Head per stage at the design rate 40.3 ft/stage
54 Stages required (exact) 36.16954876 stages
55 Stages installed 37 stages
56
57 Operating Point at the Design Frequency
58 Frequency that delivers the design rate 59.49134083 Hz
59 Design frequency (solved unless set above) 59.49134083 Hz
60 Operating rate 2999.672826 bbl/d
61 TDH at the operating point 1457.473673 ft
62 Rate as % of BEP at this speed 1.009281215
63 Range check Within recommended range
64 Pump efficiency 0.6780173968
65 Brake horsepower 50.61910691 HP
66 Pump differential pressure 675.1068527 psi
67 Sink at the operating point (drainage drawdown) 299.9672826 psi
68
69 Motor and Inverted Service
70 Minimum motor power (BHP × safety factor) 55.6810176 HP
71 Motor load at the design frequency 0.8508651209
72 Load status Optimal loading
73 Velocity past the motor 4.57420954 ft/s
74 Cooling check OK (1 ft/s or more)
75 Estimated motor temperature 192.6547767 degF
76 Packer check (pump ΔP acting from below) Within rating
77 Hydraulic thrust on the pump shaft 405.9555692 lbf
78
79 Calculation Tables (nothing to edit below)
80 System-curve rate coefficient 0.4857476636 ft per bbl/d
81 Rate grid upper bound 5500 bbl/d
82
83 System Curve and Pump Head on a Rate Grid (design frequency)
84 Rate (bbl/d) System TDH (ft) Pump head (ft) Pump − system (ft) Crossing (bbl/d)
85 0 -0.691588785 1891.516271 1892.20786
86 110 52.74304143 1894.649292 1841.906251
87 220 106.1815032 1897.310442 1791.128939
88 330 159.623361 1899.027849 1739.404488
89 440 213.0684077 1899.329641 1686.261233
90 550 266.5165062 1897.757644 1631.241138
91 660 319.9675553 1894.179214 1574.211659
92 770 373.4214747 1888.793164 1515.37169
93 880 426.8781985 1881.813191 1454.934993
94 990 480.337671 1873.452992 1393.115321
95 1100 533.7998439 1863.869008 1330.069165
96 1210 587.2646747 1852.978942 1265.714268
97 1320 640.7321257 1840.638284 1199.906159
98 1430 694.2021628 1826.702524 1132.500361
99 1540 747.6747552 1811.032111 1063.357356
100 1650 801.1498745 1793.613551 992.4636764
101 1760 854.6274947 1774.566415 919.9389201
102 1870 908.1075917 1754.016641 845.9090494
103 1980 961.590143 1732.090168 770.5000247
104 2090 1015.075128 1708.875126 693.7999977
105 2200 1068.562526 1684.295316 615.7327901
106 2310 1122.05232 1658.229907 536.1775865
107 2420 1175.544491 1630.558061 455.0135694
108 2530 1229.039024 1601.162974 372.12395
109 2640 1282.535902 1570.037506 287.5016037
110 2750 1336.035111 1537.294544 201.259433
111 2860 1389.536636 1503.053083 113.5164467
112 2970 1443.040464 1467.432117 24.391653 2999.672826
113 3080 1496.546582 1430.516046 -66.03053579
114 3190 1550.054977 1392.232512 -157.8224643
115 3300 1603.565637 1352.464782 -251.1008547
116 3410 1657.078551 1311.096119 -345.9824322
117 3520 1710.593708 1268.013258 -442.5804502
118 3630 1764.111097 1223.204392 -540.9067052
119 3740 1817.630708 1176.772845 -640.8578624
120 3850 1871.15253 1128.828165 -742.3243657
121 3960 1924.676555 1079.479896 -845.1966596
122 4070 1978.202773 1028.810528 -949.3922455
123 4180 2031.731176 976.7747332 -1054.956442
124 4290 2085.261753 923.2894763 -1161.972277
125 4400 2138.794497 868.2717166 -1270.522781
126 4510 2192.3294 811.6393536 -1380.690047
127 4620 2245.866454 753.3398361 -1492.526618
128 4730 2299.40565 693.3553812 -1606.050269
129 4840 2352.946982 631.6701985 -1721.276783
130 4950 2406.490442 568.2684976 -1838.221944
131 5060 2460.036022 503.1883046 -1956.847718
132 5170 2513.583717 436.7327274 -2076.850989
133 5280 2567.133518 369.2863526 -2197.847166
134 5390 2620.68542 301.2337891 -2319.451631
135 5500 2674.239416 0 -2674.239416
136
137 Frequency That Delivers the Design Rate (installed stages)
138 Frequency (Hz) Pump head at the design rate (ft) Crossing (Hz)
139 30 0
140 31 0
141 32 0
142 33 89.19404125
143 34 126.8048654
144 35 166.0029578
145 36 206.46
146 37 247.9298196
147 38 290.3738551
148 39 333.80176
149 40 378.2222222
150 41 423.6482372
151 42 470.1116911
152 43 517.646419
153 44 566.2831803
154 45 616.05
155 46 666.9632252
156 47 719.0016344
157 48 772.1369182
158 49 826.3430786
159 50 881.5961973
160 51 937.8742317
161 52 995.1580358
162 53 1053.449695
163 54 1112.767253
164 55 1173.127922
165 56 1234.547683
166 57 1297.041397
167 58 1360.6229
168 59 1425.305088 59.49134083
169 60 1491.1
170 61 1558.015285
171 62 1626.043937
172 63 1695.175912
173 64 1765.401792
174 65 1836.71274
175 66 1909.100453
176 67 1982.557125
177 68 2057.075408
178 69 2132.648382
179 70 2209.269521
180 71 2286.932665
181 72 2365.632
182 73 2445.363798
183 74 2526.13152
184 75 2607.940164
185
186 Pump Curve at the Design Frequency (installed stages)
187 Rate (bbl/d) Head (ft) Efficiency
188 0 1891.516271 0
189 495.7611736 1898.791334 0.2072182846
190 991.5223472 1873.328615 0.3766741649
191 1487.283521 1818.765645 0.5089734254
192 1983.044694 1731.464894 0.6025776932
193 2478.805868 1615.063893 0.6598836336
194 2974.567042 1465.92511 0.6780755657
195 3470.328215 1287.686077 0.6596014883
196 3966.089389 1076.709262 0.6027639353
197 4461.850563 836.6321969 0.5092396892
198 4957.611736 563.8173501 0.3767662571
199 5453.37291 261.9022529 0.2079497094
200
201 Chart Markers
202 Marker Rate (bbl/d) Head (ft)
203 Operating point 2999.672826 1457.473673
204 BEP at the design frequency 2972.088236 1466.743322
205 Minimum rate, axis 2181.349164 0
206 Minimum rate, pump curve 2181.349164 1688.564172
207 Maximum rate, axis 3767.784919 0
208 Maximum rate, pump curve 3767.784919 1164.801003

Description

Sizes an ESP that runs inverted in a downhole water sink or downhole water loop: water drained below the oil–water contact is pumped down through a packer and re-injected into the base of the same aquifer. Nothing is lifted to surface, so the system curve is drainage drawdown plus injection build-up plus friction. Design by rate, or by the sink wanted at the drainage perforations (rate = PI × sink). Returns the TDH split into sink head, injection head, static head and friction, the stage count, the drive frequency that delivers the design rate, the operating point, efficiency, brake horsepower, the sink it makes, motor loading and cooling, and the packer and shaft-thrust checks, with a performance chart.

Parameters:

  • Q: Target water rate, drainage = injection (bbl/d)
  • sink: Target sink at the drainage perforations, 0 to design by rate (psi)
  • SG: Water specific gravity, not the psi/ft gradient (dimensionless)
  • P_drain, PI: Drainage zone static pressure (psi) and productivity index (bbl/d/psi)
  • P_inj, II: Injection zone static pressure, 0 for the same aquifer (psi), and injectivity index (bbl/d/psi)
  • ΔZ: Vertical distance from the drainage to the injection perforations (ft)
  • Pump curve: One stage at catalog frequency for water: rate, head and brake horsepower. The shipped curve is example data.

Method: TDH(Q) = [(P_inj + Q/II) − (P_drain − Q/PI)] / (0.433 × SG) − ΔZ + friction(Q). In one connected aquifer the static terms cancel, so with II close to PI the pump needs about twice the sink head: it pays for the sink and for re-injecting the same water. Stages are set at catalog frequency; the frequency that delivers the design rate and the operating point at the design frequency are each found on a table, by linear interpolation between the two bracketing rows, with the affinity laws moving the curve with speed. Two checks flag an SG outside 0.90–1.30 (a psi/ft gradient typed as SG) and a static head between the zones beyond 5 ft (pressures and spacing that do not describe one connected aquifer). The functions the PO.ESP.* catalog lacks are defined as _PO.ESP.* LAMBDAs. The rate cases, the variable-speed chart and the guide are in the Inverted ESP Sizing workbook.

How to use this blueprint
  1. In Excel, go to the Petroleum Office ribbon tab and click Blueprint Manager
  2. Search for Inverted ESP Sizing for a Downhole Water Sink
  3. Click on the blueprint to preview
  4. Click Insert to place it into your worksheet. Modify the input values to match your data.
Tags:
ESPdownhole-water-sinkinverted-esppump-sizingTDHsystem-curveoperating-pointBEPwaterinjection

Need a custom calculation? Request a Blueprint