Inverted ESP Sizing — Downhole Water Sink

Sizes an electric submersible pump that runs inverted in a downhole water sink (DWS) or downhole water loop (DWL) completion: water drained below the oil–water contact is pumped down through an isolation 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 a short friction path — for a hydrostatically connected aquifer, a straight line through the origin.

Inverted ESP Sizing Excel workbook

DwsInvertedEspSizing.xlsx

Inverted ESP Sizing — Downhole Water Sink: Single-stage catalog curve (Pump Curve)

Inverted ESP Sizing — Downhole Water Sink: Pump head, system curve and efficiency (Performance Chart)

Inverted ESP Sizing — Downhole Water Sink: Brake horsepower (installed stages, fluid SG) (Performance Chart)

Inverted ESP Sizing — Downhole Water Sink: Tornado chart (VSD Chart)

Inverted ESP Sizing — Downhole Water Sink: Guide sheet

Inverted ESP Sizing — Downhole Water Sink: Inputs sheet

Inverted ESP Sizing — Downhole Water Sink: Pump Curve sheet

Inverted ESP Sizing — Downhole Water Sink: Design sheet

Inverted ESP Sizing — Downhole Water Sink: Calc sheet

Description Preview Requirements

Design by rate, or by sink: enter the drawdown wanted at the drainage perforations and the design rate becomes PI × sink. From the loop hydraulics (or a known TDH) and a vendor single-stage curve it returns the design TDH, split in feet into sink head, injection head, static head and friction; the stage count, brake horsepower, BEP and operating-point efficiency; the sink at the operating point; the drive frequency that delivers each rate; motor loading, motor cooling velocity, packer differential and shaft thrust. With injectivity close to the PI the design TDH is about twice the sink head, because the pump also has to re-inject the water it drains. Two print-ready charts: the pump performance curve against the system curve, and the variable-speed (tornado) chart.

Two input checks: an SG outside the plausible brine range (a psi/ft gradient typed into the SG cell), and a static head between the zones that is not about zero (zone pressures and spacing that do not describe one connected aquifer). An injection static pressure of 0 is computed for the same-aquifer case.

The functions the PO.ESP.* catalog lacks are defined as workbook LAMBDAs: PO.ESP.DWS.TDH, PO.ESP.Affinity.Rate, PO.ESP.Affinity.Head, PO.ESP.Affinity.Power, PO.ESP.Curve.HeadAtSpeed, PO.ESP.Curve.PowerAtSpeed, PO.ESP.Motor.CoolingVelocity, PO.ESP.Shaft.Thrust.

Inputs

Named cells you can edit — every result recalculates from them.

Name	Description	Default	Unit
`DWS_Q`	Target water rate (drainage = injection)	3000	bbl/d
`DWS_Sink`	Target sink at the drainage perforations (0 = design by rate)	0	psi
`DWS_SG`	Water specific gravity	1.07	—
`DWS_Pdr`	Drainage zone static pressure	3200	psi
`DWS_PI`	Drainage productivity index	10	bbl/d/psi
`DWS_Pinj`	Injection zone static pressure (0 = same aquifer as the drain)	3246	psi
`DWS_II`	Injectivity index	8	bbl/d/psi
`DWS_dZ`	Vertical distance, drainage to injection perforations	100	ft
`DWS_FlowID`	Flow-path ID, pump discharge to injection perforations	3.958	in
`DWS_FlowL`	Flow-path length	150	ft
`DWS_TDHKnown`	Known TDH at the design rate (0 = use loop hydraulics)	0	ft
`DWS_Fbase`	Catalog curve frequency	60	Hz
`DWS_FreqSet`	Design frequency (0 = frequency that delivers the design rate)	0	Hz
`DWS_StagesSet`	Stages installed (0 = minimum at catalog frequency)	0	stages
`DWS_MotorHP`	Motor nameplate power at catalog frequency	60	HP
`DWS_SF`	Motor sizing safety factor	1.10	—
`DWS_MotorOD`	Motor OD	5.62	in
`DWS_CasingID`	Casing (or shroud) ID at the motor	6.276	in
`DWS_Temp`	Water temperature at the motor	180	degF
`DWS_Shaft`	Pump shaft diameter	0.875	in
`DWS_PackerRating`	Packer differential pressure rating	5000	psi
`DWS_Qmin`	Pump recommended range — minimum rate	2200	bbl/d
`DWS_Qmax`	Pump recommended range — maximum rate	3800	bbl/d
`DWS_Cases`	Rate cases (five)	2000–4000	bbl/d
`DWS_VsdF`	Tornado chart frequencies (seven)	40–70	Hz

The single-stage curve (DWS_CurveQ, DWS_CurveH, DWS_CurveP) on the Pump Curve sheet is example data to be replaced with the vendor's curve.

7 sheets, shown with the values the file opens with

	A
1	Inverted ESP Sizing — Downhole Water Sink / Downhole Water Loop
2
3	What this workbook does
4	Sizes an electric submersible pump that runs inverted in a downhole water sink (DWS) or downhole water loop (DWL) completion. Water is drained from the water zone below the oil–water contact, boosted by the pump and re-injected into the base of the same aquifer through an isolation packer. Nothing is lifted to surface, so well depth drops out of the sizing: the pump only overcomes the drawdown at the drainage completion, the pressure build-up at the injection completion and a short friction path.
5	It returns the design TDH, stage count, brake horsepower, best efficiency point (BEP) and efficiency at the operating point, the drive frequency that delivers each target rate, motor loading and the inverted-service checks, plus two printable charts: the pump performance curve with the system curve, and the variable-speed (tornado) chart.
6
7	Loop hydraulics
8	TDH(Q) = [ (P_inj + Q / II) − (P_drain − Q / PI) ] / (0.433 × SG) − ΔZ + h_friction(Q), where P_drain and P_inj are the static pressures at the drainage and injection perforations, PI and II the drainage productivity index and the injectivity index, and ΔZ the vertical distance from the drainage perforations down to the injection perforations.
9	In one hydraulically connected aquifer P_inj − P_drain = 0.433 × SG × ΔZ, the static terms cancel and TDH ≈ Q × (1/PI + 1/II) / (0.433 × SG): a straight line through the origin. The system curve is always built as static head + (coefficient × Q) + friction(Q). If you enter a known TDH, the coefficient is calibrated so the curve passes through your TDH at the design rate.
10
11	Why the TDH is about twice the sink
12	The pump lifts water from the drainage flowing pressure (P_drain − Q/PI) to the injection flowing pressure (P_inj + Q/II), so it pays for both ends of the loop: the sink it makes at the drain, and the build-up it needs to push the same water into the injection zone. With II close to PI the two are equal.
13	Example: 2,500 bbl/d with PI = II = 22.2 bbl/d/psi and SG 1.07 in one aquifer. The sink is 2,500 / 22.2 = 113 psi, which is 243 ft of this water, and re-injecting takes another 113 psi, or 243 ft. The design TDH is therefore about 486 ft plus friction: twice the sink head. Put the other way, a pump making 243 ft in this loop creates a sink of only about 56 psi. The Design sheet splits the TDH into sink head, injection head, static head and friction, all in feet, and shows the share of the head that goes into the sink.
14
15	How to use it
16	1. Inputs — edit the blue cells on a yellow background; every other cell is calculated. Design either by rate (the target water rate) or by sink: enter the drawdown you want below static at the drainage perforations, and the design rate becomes PI × sink. Two checks sit beside the inputs: the SG against a plausible brine range (SG is not the psi/ft gradient), and the static head between the zones, which is about zero when both perforation sets are in one connected aquifer. Enter 0 for the injection zone static pressure to compute it for that case.
17	2. Pump Curve — replace the EXAMPLE curve with the vendor's single-stage curve: 12 points, ascending rate from shut-in to run-out, head and brake horsepower per stage for water (SG 1.0) at the catalog frequency on the Inputs sheet. Enter the vendor's recommended operating range for the pump.
18	3. Design — the sizing summary. Stages are set at the catalog frequency and the drive frequency is then solved so the pump delivers exactly the design rate (or enter a design frequency on the Inputs sheet). The rate-case table shows the frequency, loading and range check for each rate case.
19	4. Performance Chart and VSD Chart — both are set up to print on one page (File › Print).
20
21	Choosing the sink
22	• A stronger sink is not always better. A drainage sink much stronger than the oil completion's drawdown pulls oil down into the water drain (reverse coning) and sends it to the injection zone; one too weak lets water cone up into the oil completion. The sinks that keep both completions clean form the inflow performance window of the downhole water sink literature (Wojtanowicz and co-workers). This workbook sizes the pump for the sink or rate you choose; it does not compute that window, so check the sink with a coning analysis or a near-well model first.
23
24	Inverted-service notes
25	• Thrust: inverting the pump puts impeller weight against the hydraulic thrust. Prefer compression (fixed-impeller) stages, size the protector thrust bearing for the load on the Design sheet in both directions, and ask the vendor for the recommended operating range in inverted service.
26	• Motor cooling: with the motor on top, drainage water must flow down past it. Keep the annular velocity at 1 ft/s or more; if the motor sits in a dead leg, fit a shroud.
27	• Packer: the packer below the pump carries the pump differential pressure from below, plus start/stop surges.
28	• Injectivity: injectivity usually declines with oil carry-over and solids. Size for the end-of-life injectivity index, and stay below the injection zone fracture pressure. PI and II from separate tests ignore sink–source interference, which normally makes the computed head conservative.
29	• Gauges: the discharge sits below the intake, so a gauge-to-gauge pressure difference also includes the fluid column over the pump length.
30
31	Requirements
32	The workbook calls Petroleum Office functions (PO.ESP.*) and defines eight LAMBDA functions (Formulas › Name Manager: PO.ESP.DWS.TDH, PO.ESP.Affinity.Rate/Head/Power, PO.ESP.Curve.HeadAtSpeed/PowerAtSpeed, PO.ESP.Motor.CoolingVelocity, PO.ESP.Shaft.Thrust). It opens with the example results already calculated; recalculating after an edit needs the Petroleum Office add-in and an Excel version with LAMBDA (Microsoft 365 or Excel 2024).

	A	B	C	D	E	F	G	H	I
1	Inputs
2	Blue cells on a yellow background are inputs; everything else in the workbook recalculates from them and from the Pump Curve sheet. Field units. The defaults describe an example same-aquifer loop.
3
4	Loop hydraulics
5	Target water rate (drainage = injection)	3000	bbl/d	The design rate unless a target sink is set
6	Target sink at the drainage perforations (0 = design by rate)	0	psi	Drawdown below static you want at the drain; the design rate becomes PI × sink
7	Water specific gravity	1.07	—	Brine at loop conditions
8	Water pressure gradient (from SG)	0.463	psi/ft	Calculated: 0.433 × SG. Enter the SG above, not this
9	Drainage zone static pressure	3200	psi	At the drainage (water-sink) perforations
10	Drainage productivity index	10	bbl/d/psi	Drainage perforations
11	Injection zone static pressure (0 = same aquifer as the drain)	3246	psi	At the injection perforations; 0 computes P_drain + gradient × ΔZ
12	Injectivity index	8	bbl/d/psi	Use the end-of-life value — injectivity usually declines
13	Vertical distance, drainage to injection perforations	100	ft	Positive when injection is deeper
14	Static head between zones (≈ 0 in one aquifer)	-0.7	ft	Consistent with one connected aquifer
15	Flow-path ID, pump discharge to injection perforations	3.958	in	Stinger / tailpipe bore
16	Flow-path length	150	ft	Pump discharge to injection perforations
17	Known TDH at the design rate (0 = use loop hydraulics)	0	ft	Overrides the hydraulic TDH and calibrates the system curve
18
19	Pump and drive
20	Catalog curve frequency	60	Hz	Frequency of the curve on the Pump Curve sheet
21	Design frequency (0 = frequency that delivers the design rate)	0	Hz	Fixed-speed design: enter the supply frequency
22	Stages installed (0 = minimum at catalog frequency)	0	stages	Enter the stage count of a candidate pump to check it
23
24	Motor and installation
25	Motor nameplate power at catalog frequency	60	HP	Available power scales with frequency on a VSD
26	Motor sizing safety factor	1.1	—	Minimum motor power = BHP × factor
27	Motor OD	5.62	in
28	Casing (or shroud) ID at the motor	6.276	in	7 in 26 lb/ft casing
29	Water temperature at the motor	180	degF
30	Pump shaft diameter	0.875	in	For the shaft thrust estimate
31	Packer differential pressure rating	5000	psi
32
33	Rate cases and chart frequencies
34	Rate cases	2,000	2,500	3,000	3,500	4,000	bbl/d
35	VSD chart frequencies	40	45	50	55	60	65	70	Hz

	A	B	C	D
1	Pump Curve — one stage at catalog frequency
2	EXAMPLE DATA — replace with the vendor's single-stage curve: 12 points, ascending rate from shut-in to run-out, head and brake horsepower per stage for water (SG 1.0) at the catalog frequency on the Inputs sheet. Efficiency is calculated from head and power.
3
4	Pump
5	Pump model	Generic 538-series mixed-flow stage (EXAMPLE)
6	Recommended range — minimum rate	2200	bbl/d
7	Recommended range — maximum rate	3800	bbl/d
8
9	Single-stage performance
10	Rate (bbl/d)	Head (ft/stage)	BHP (HP/stage)	Efficiency
11	0	52.0	0.800	0.0%
12	500	52.2	0.924	20.7%
13	1,000	51.5	1.003	37.7%
14	1,500	50.0	1.081	50.9%
15	2,000	47.6	1.159	60.3%
16	2,500	44.4	1.234	66.0%
17	3,000	40.3	1.308	67.8%
18	3,500	35.4	1.378	66.0%
19	4,000	29.6	1.441	60.3%
20	4,500	23.0	1.491	50.9%
21	5,000	15.5	1.509	37.7%
22	5,500	7.2	1.397	20.8%
23
24	Curve summary
25	Best efficiency point (BEP) rate	2,998	bbl/d
26	Efficiency at BEP	67.8%
27	Head per stage at BEP	40.3	ft/stage
28	Recommended range as % of BEP	73% – 127%

Head (ft/stage) Efficiency

	A	B	C	D	E	F	G	H
1	Design Summary — inverted ESP for a downhole water sink
2	Everything on this sheet recalculates from the Inputs and Pump Curve sheets.
3
4	Loop hydraulics at the design rate
5	Design basis	Target rate (Inputs)
6	Design water rate	3,000	bbl/d
7	Drainage sink: drawdown (Q / PI)	300	psi
8	Injection pressure build-up (Q / II)	375	psi
9	Drainage flowing pressure (≈ pump intake)	2,900	psi
10	Injection flowing pressure (≈ pump discharge)	3,621	psi
11	Input checks	SG and zone pressures pass
12
13	TDH at the design rate, in feet of water
14	Sink head (drainage drawdown)	647.7	ft
15	Injection head (build-up)	809.6	ft
16	Static head between zones	-0.7	ft
17	Flow-path friction	1.1	ft
18	TDH from loop hydraulics (sum of the four above)	1,457.6	ft
19	TDH basis	Loop hydraulics
20	Design TDH	1,458	ft
21	Share of the rate-driven head that makes the sink	44%
22	The pump pays for both ends of the loop: the sink it makes at the drain, and the build-up that pushes the same water into the injection zone. With II close to PI the design TDH is about twice the sink head.
23
24	Pump sizing at catalog frequency
25	Pump model	Generic 538-series mixed-flow stage (EXAMPLE)
26	Best efficiency point (BEP) rate	2,998	bbl/d
27	Efficiency at BEP	67.8%
28	Head per stage at the design rate	40.30	ft/stage
29	Stages required (exact)	36.2	stages
30	Stages installed	37	stages
31	Pump head at the design rate	1,491	ft
32
33	Operating point at the design frequency
34	Design frequency (solved unless set on Inputs)	59.5	Hz
35	Operating rate	3,000	bbl/d
36	TDH at the operating point	1,457	ft
37	Rate as % of BEP at this speed	101%
38	Recommended range at this speed	2,181 – 3,768	bbl/d
39	Range check	Within recommended range
40	Pump efficiency	67.8%
41	Hydraulic horsepower	34.3	HP
42	Brake horsepower	50.6	HP
43	Pump differential pressure	675	psi
44	Sink at the operating point (drainage drawdown)	300	psi
45
46	Motor
47	Minimum motor power (BHP × safety factor)	55.7	HP
48	Motor power available at the design frequency	59.5	HP
49	Motor load	85%
50	Load status	Optimal loading
51	Velocity past the motor	4.57	ft/s
52	Cooling check	OK (1 ft/s or more)
53	Estimated motor temperature	193	degF
54
55	Inverted-service checks
56	Packer differential (pump ΔP, acting from below)	675	psi
57	Packer check	Within rating
58	Hydraulic thrust on the pump shaft	406	lbf
59	Size the protector thrust bearing for this load in the inverted direction; compression (fixed-impeller) stages are preferred for inverted service. Confirm the recommended operating range for inverted service with the vendor.
60
61	Rate cases (installed stages on a variable-speed drive)
62	Case	Rate (bbl/d)	TDH (ft)	Frequency (Hz)	% of BEP	Range check	BHP (HP)	Motor load
63	Design rate	3,000	1,458	59.5	101%	Within range	50.6	85%
64	Case 1	2,000	971	46.5	86%	Within range	22.9	49%
65	Case 2	2,500	1,214	53.1	94%	Within range	35.3	66%
66	Case 3	3,000	1,458	59.5	101%	Within range	50.6	85%
67	Case 4	3,500	1,701	65.6	107%	Within range	69.2	105%
68	Case 5	4,000	1,944	71.6	112%	Within range	91.2	127%

	A	B	C	D	E	F
1	Pump performance — Generic 538-series mixed-flow stage (EXAMPLE)
2
3	Stages installed	37		Design frequency	59.5	Hz
4	Operating rate	3,000	bbl/d	TDH at operating point	1,457	ft
5	Pump efficiency	67.8%		Brake horsepower	50.6	HP
6	BEP rate at this speed	2,972	bbl/d	Water specific gravity	1.07
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45

Pump head (installed stages) System curve (loop TDH) Minimum rate Maximum rate BEP Operating point Efficiency (right axis)

Brake horsepower Operating point

	A
1	Variable-speed performance — 37 stages, Generic 538-series mixed-flow stage (EXAMPLE)
2	Pump head for the installed stages at each drive frequency (affinity laws: rate ∝ f, head ∝ f², power ∝ f³). Dashed lines bound the recommended operating range; the red line is the loop system curve.
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31

Series Series Series Series Series Series Series System curve (loop TDH) Minimum rate Maximum rate Operating point

	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O
1	Calc — helper tables
2	Intermediate results behind the Design and chart sheets. Nothing here needs editing. Rate solves are tabulated and interpolated between the bracketing rows, so there is no iteration and no circular reference.
3
4	Design scalars
5	Design water rate	3000	bbl/d
6	Water pressure gradient	0.4632034632	psi/ft
7	Injection zone static pressure used (0 on Inputs = same aquifer)	3246	psi
8	Static head between zones (zero rate)	-0.691588785	ft
9	Sink head: drainage drawdown at the design rate	647.6635514	ft
10	Injection head: build-up at the design rate	809.5794393	ft
11	Flow-path friction at the design rate	1.0814132	ft
12	TDH from loop hydraulics at the design rate	1457.632815	ft
13	Design TDH at the design rate	1457.632815	ft
14	System-curve rate coefficient	0.4857476636	ft per bbl/d
15	Head per stage at the design rate, catalog frequency	40.3	ft/stage
16	Stages required (exact)	36.16954876	stages
17	Stages installed	37	stages
18	Frequency that delivers the design rate	59.49134083	Hz
19	Design frequency	59.49134083	Hz
20	Speed ratio (design / catalog frequency)	0.9915223472	—
21	Rate grid upper bound	6416.666667	bbl/d
22	Operating rate at design frequency	2999.577284	bbl/d
23	TDH at the operating point	1457.4272	ft
24	Brake horsepower at the operating point	50.61857027	HP
25	Pump efficiency at the operating point	0.6780177872	fraction
26	Share of the loop's rate-dependent head that makes the sink	0.4444444444	fraction
27	Sink at the operating point (drainage drawdown)	299.9577284	psi
28	SG outside the plausible brine range	FALSE	TRUE = check
29	Static head between zones not ≈ 0	FALSE	TRUE = check
30
31
32
33
34	System curve and pump head on a rate grid (design frequency)
35	Rate (bbl/d)	Friction (ft)	System TDH (ft)	Pump head (ft)	Pump − system (ft)
36	0	0	-0.691588785	1891.516271	1892.20786
37	128.3333333	0.003175012017	61.64920305	1895.13833	1833.489127
38	256.6666667	0.0114459242	123.9950908	1898.011074	1774.015983
39	385	0.02423369818	186.3454954	1899.385188	1713.039693
40	513.3333333	0.04126257791	248.7001411	1898.511825	1649.811684
41	641.6666667	0.06235049152	311.0588458	1894.90692	1583.848074
42	770	0.08736252678	373.4214747	1888.793164	1515.37169
43	898.3333333	0.1161921392	435.7879211	1880.509903	1444.721982
44	1026.666667	0.1487516697	498.1580975	1870.394531	1372.236434
45	1155	0.1849668991	560.5319295	1858.596268	1298.064338
46	1283.333333	0.2247736373	622.9093531	1844.921934	1222.012581
47	1411.666667	0.2681154502	685.2903117	1829.142054	1143.851743
48	1540	0.3149420707	747.6747552	1811.032111	1063.357356
49	1668.333333	0.3652082463	810.0626382	1790.548723	980.4860845
50	1796.666667	0.4188728767	872.4539196	1767.877231	895.4233112
51	1925	0.475898354	934.8485619	1743.217621	808.3690588
52	2053.333333	0.5362500446	997.2465304	1716.759147	719.5126163
53	2181.666667	0.5998958782	1059.647793	1688.491855	628.8440616
54	2310	0.6668060136	1122.05232	1658.229907	536.1775865
55	2438.333333	0.7369525657	1184.460083	1625.781421	441.3213375
56	2566.666667	0.8103093784	1246.871057	1590.974885	344.103828
57	2695	0.8868518344	1309.285216	1553.860775	244.5755583
58	2823.333333	0.966556694	1371.702538	1514.626058	142.9235199
59	2951.666667	1.049401958	1434.123	1473.459694	39.33669365
60	3080	1.135366748	1496.546582	1430.516046	-66.03053579
61	3208.333333	1.224431206	1558.973263	1385.710779	-173.2624839
62	3336.666667	1.316576404	1621.403025	1338.858874	-282.5441511
63	3465	1.411784265	1683.83585	1289.774957	-394.060893
64	3593.333333	1.510037496	1746.27172	1238.326388	-507.945332
65	3721.666667	1.611319525	1808.710619	1184.619473	-624.0911451
66	3850	1.715614447	1871.15253	1128.828165	-742.3243657
67	3978.333333	1.822906976	1933.59744	1071.126372	-862.4710677
68	4106.666667	1.933182403	1996.045332	1011.621188	-984.4241435
69	4235	2.046426553	2058.496193	950.2184775	-1108.277715
70	4363.333333	2.162625751	2120.950009	886.7863739	-1234.163635
71	4491.666667	2.281766793	2183.406767	821.1932353	-1362.213532
72	4620	2.403836913	2245.866454	753.3398361	-1492.526618
73	4748.333333	2.528823758	2308.329057	683.1930499	-1625.136007
74	4876.666667	2.656715363	2370.794566	610.7278022	-1760.066764
75	5005	2.787500131	2433.262967	535.9243539	-1897.338613
76	5133.333333	2.921166809	2495.734251	459.0136681	-2036.720583
77	5261.666667	3.057704472	2558.208405	380.5798983	-2177.628507
78	5390	3.197102504	2620.68542	301.2337891	-2319.451631
79	5518.333333	3.339350585	2683.165285	0	-2683.165285
80	5646.666667	3.484438671	2745.64799	0	-2745.64799
81	5775	3.632356984	2808.133525	0	-2808.133525
82	5903.333333	3.783095999	2870.621881	0	-2870.621881
83	6031.666667	3.936646432	2933.113048	0	-2933.113048
84	6160	4.092999226	2995.607018	0	-2995.607018
85	6288.333333	4.252145546	3058.103781	0	-3058.103781
86	6416.666667	4.414076763	3120.603329	0	-3120.603329
87
88	Crossing index (last row with pump head above system)	24
89
90	Frequency that delivers each rate (installed stages)
91		Design	Case 1	Case 2	Case 3	Case 4	Case 5
92	Rate (bbl/d)	3000	2000	2500	3000	3500	4000
93	System TDH (ft)	1457.632815	971.3145053	1214.449373	1457.632815	1700.863513	1944.140381
94	Frequency (Hz)	Pump head at the rate (ft)
95	30	0	273.8	143.375	0	0	0
96	31	0	307.9304925	178.0141427	0	0	0
97	32	0	343.1719637	213.6294763	0	0	0
98	33	89.19404125	379.4845278	250.2322298	89.19404125	0	0
99	34	126.8048654	416.8329919	287.8341529	126.8048654	0	0
100	35	166.0029578	455.1896687	326.4664521	166.0029578	0	0
101	36	206.46	494.5632235	366.1699128	206.46	0	0
102	37	247.9298196	534.9797609	406.9811226	247.9298196	0	0
103	38	290.3738551	576.4628433	448.9314197	290.3738551	0	0
104	39	333.80176	619.0336163	492.0175913	333.80176	143.0472358	0
105	40	378.2222222	662.7111111	536.2061932	378.2222222	187.6392798	0
106	41	423.6482372	707.5071481	581.4657478	423.6482372	233.7199923	0
107	42	470.1116911	753.4115166	627.7677755	470.1116911	281.015	0
108	43	517.646419	800.4098506	675.0864686	517.646419	329.3155958	0
109	44	566.2831803	848.4890902	723.4096282	566.2831803	378.5889667	158.5671844
110	45	616.05	897.6373367	772.7550367	616.05	428.8435751	208.4260854
111	46	666.9632252	947.8437255	823.1435109	666.9632252	480.0871474	259.9589603
112	47	719.0016344	999.0983171	874.5940957	719.0016344	532.3269191	312.9087967
113	48	772.1369182	1051.392	927.1242492	772.1369182	585.5793075	367.04
114	49	826.3430786	1104.719044	980.7500043	826.3430786	639.8742462	422.1714348
115	50	881.5961973	1159.084517	1035.486111	881.5961973	695.2405268	478.2745473
116	51	937.8742317	1214.495623	1091.341859	937.8742317	751.7046829	535.3568687
117	52	995.1580358	1270.959012	1148.308937	995.1580358	809.2912066	593.425351
118	53	1053.449695	1328.480832	1206.375521	1053.449695	868.0217394	652.4864216
119	54	1112.767253	1387.066775	1265.53066	1112.767253	927.8936876	712.5471912
120	55	1173.127922	1446.722121	1325.764204	1173.127922	988.8824258	773.6274898
121	56	1234.547683	1507.45177	1387.066722	1234.547683	1050.964139	835.7541174
122	57	1297.041397	1569.260281	1449.429451	1297.041397	1114.116682	898.9521311
123	58	1360.6229	1632.151896	1512.844228	1360.6229	1178.319439	963.2448596
124	59	1425.305088	1696.130572	1577.303444	1425.305088	1243.553191	1028.65405
125	60	1491.1	1761.2	1642.8	1491.1	1309.8	1095.2
126	61	1558.015285	1827.362514	1709.329378	1558.015285	1377.048589	1162.894707
127	62	1626.043937	1894.615904	1776.895692	1626.043937	1445.309997	1231.72197
128	63	1695.175912	1962.957021	1845.504843	1695.175912	1514.599872	1301.659869
129	64	1765.401792	2032.382911	1915.162367	1765.401792	1584.932885	1372.687855
130	65	1836.71274	2102.890803	1985.873456	1836.71274	1656.322803	1444.786641
131	66	1909.100453	2174.478094	2057.642991	1909.100453	1728.782561	1517.938111
132	67	1982.557125	2247.142334	2130.475557	1982.557125	1802.324318	1592.125231
133	68	2057.075408	2320.881222	2204.375473	2057.075408	1876.959521	1667.331967
134	69	2132.648382	2395.692585	2279.346806	2132.648382	1952.698952	1743.543599
135	70	2209.269521	2471.574378	2355.393391	2209.269521	2029.552778	1820.758675
136	71	2286.932665	2548.52467	2432.518846	2286.932665	2107.527499	1898.990599
137	72	2365.632	2626.541636	2510.726591	2365.632	2186.617063	1978.252894
138	73	2445.363798	2705.623553	2590.019854	2445.363798	2266.812738	2058.558345
139	74	2526.13152	2785.76879	2670.401693	2526.13152	2348.106267	2139.919044
140	75	2607.940164	2866.975804	2751.875	2607.940164	2430.489834	2222.346438
141
142	Crossing index	30	17	24	30	36	42
143	Required frequency (Hz)	59.5	46.5	53.1	59.5	65.6	71.6
144
145	Pump curve at design frequency (installed stages)
146	Rate (bbl/d)	Head (ft)	BHP (HP)	Efficiency	System TDH (ft)
147	0	1891.516271	30.8732969	0	-0.691588785
148	495.7611736	1898.791334	35.65865792	0.2072182846	240.1619306
149	991.5223472	1873.328615	38.70739599	0.3766741649	481.0775435
150	1487.283521	1818.765645	41.71754244	0.5089734254	722.0481945
151	1983.044694	1731.464894	44.72768889	0.6025776932	963.0705235
152	2478.805868	1615.063893	47.62206047	0.6598836336	1204.142312
153	2974.567042	1465.92511	50.47784044	0.6780755657	1445.261916
154	3470.328215	1287.686077	53.17925392	0.6596014883	1686.428037
155	3966.089389	1076.709262	55.61052605	0.6027639353	1927.639607
156	4461.850563	836.6321969	57.5401071	0.5092396892	2168.895722
157	4957.611736	563.8173501	58.23475628	0.3767662571	2410.195599
158	5453.37291	261.9022529	53.91249472	0.2079497094	2651.538552
159
160	Chart markers
161		Rate (bbl/d)	Head (ft)	BHP (HP)	Efficiency
162	Operating point	2999.577284	1457.4272	50.61857027	0.6780177872
163	Minimum rate, axis	2181.349164	0
164	Minimum rate, on the pump curve	2181.349164	1688.564172
165	Maximum rate, axis	3767.784919	0
166	Maximum rate, on the pump curve	3767.784919	1164.801003
167	BEP at design frequency	2972.088236	1466.743322
168
169	Tornado chart — installed stages across drive frequencies
170		40 Hz		45 Hz		50 Hz		55 Hz		60 Hz		65 Hz		70 Hz
171		Rate	Head	Rate	Head	Rate	Head	Rate	Head	Rate	Head	Rate	Head	Rate	Head
172		0	855.1111111	0	1082.25	0	1336.111111	0	1616.694444	0	1924	0	2258.027778	0	2618.777778
173		333.3333333	858.4	375	1086.4125	416.6666667	1341.25	458.3333333	1622.9125	500	1931.4	541.6666667	2266.7125	583.3333333	2628.85
174		666.6666667	846.8888889	750	1071.84375	833.3333333	1323.263889	916.6666667	1601.149306	1000	1905.5	1083.333333	2236.315972	1166.666667	2593.597222
175		1000	822.2222222	1125	1040.625	1250	1284.722222	1375	1554.513889	1500	1850	1625	2171.180556	1750	2518.055556
176		1333.333333	782.7555556	1500	990.675	1666.666667	1223.055556	1833.333333	1479.897222	2000	1761.2	2166.666667	2066.963889	2333.333333	2397.188889
177		1666.666667	730.1333333	1875	924.075	2083.333333	1140.833333	2291.666667	1380.408333	2500	1642.8	2708.333333	1928.008333	2916.666667	2236.033333
178		2000	662.7111111	2250	838.74375	2500	1035.486111	2750	1252.938194	3000	1491.1	3250	1749.971528	3500	2029.552778
179		2333.333333	582.1333333	2625	736.7625	2916.666667	909.5833333	3208.333333	1100.595833	3500	1309.8	3791.666667	1537.195833	4083.333333	1782.783333
180		2666.666667	486.7555556	3000	616.05	3333.333333	760.5555556	3666.666667	920.2722222	4000	1095.2	4333.333333	1285.338889	4666.666667	1490.688889
181		3000	378.2222222	3375	478.6875	3750	590.9722222	4125	715.0763889	4500	851	4875	998.7430556	5250	1158.305556
182		3333.333333	254.8888889	3750	322.59375	4166.666667	398.2638889	4583.333333	481.8993056	5000	573.5	5416.666667	673.0659722	5833.333333	780.5972222
183		3666.666667	118.4	4125	149.85	4583.333333	185	5041.666667	223.85	5500	266.4	5958.333333	312.65	6416.666667	362.6
184
185	Recommended-range boundaries across frequencies
186	Frequency (Hz)	Minimum rate	Head at minimum	Maximum rate	Head at maximum
187	40	1466.666667	763.361123	2533.333333	526.5798109
188	45	1650	966.1289213	2850	666.4525731
189	50	1833.333333	1192.751755	3166.666667	822.7809545
190	55	2016.666667	1443.229623	3483.333333	995.5649549
191	60	2200	1717.562527	3800	1184.804574
192	65	2383.333333	2015.750465	4116.666667	1390.499813
193	70	2566.666667	2337.793439	4433.333333	1612.650671

Name	Refers To	Comment
PO.ESP.Affinity.Head	=LAMBDA(h, f, f_base, h*(f/f_base)^2)
PO.ESP.Affinity.Power	=LAMBDA(p, f, f_base, p*(f/f_base)^3)
PO.ESP.Affinity.Rate	=LAMBDA(q, f, f_base, q*f/f_base)
PO.ESP.Curve.HeadAtSpeed	=LAMBDA(q, f, f_base, curve_q, curve_head, IF(qf_base/f>MAX(curve_q), 0, PO.ESP.Affinity.Head(PO.ESP.Curve.Head(qf_base/f, curve_q, curve_head), f, f_base)))
PO.ESP.Curve.PowerAtSpeed	=LAMBDA(q, f, f_base, curve_q, curve_hp, IF(qf_base/f>MAX(curve_q), NA(), PO.ESP.Affinity.Power(PO.ESP.Curve.Power(qf_base/f, curve_q, curve_hp), f, f_base)))
PO.ESP.DWS.TDH	=LAMBDA(q, p_drain, pi_drain, p_inj, ii_inj, dz, sg, h_fric, PO.ESP.Head.FromPressure((p_inj + q/ii_inj) - (p_drain - q/pi_drain), sg) - dz + h_fric)
PO.ESP.Motor.CoolingVelocity	=LAMBDA(q, casing_id, motor_od, 0.0119*q/(casing_id^2 - motor_od^2))
PO.ESP.Shaft.Thrust	=LAMBDA(dp, d_shaft, dpPI()/4d_shaft^2)
DWS_BHPop	Calc!$B$24
DWS_Cases	Inputs!$B$34:$F$34
DWS_CasingID	Inputs!$B$28
DWS_CurveEff	'Pump Curve'!$D$11:$D$22
DWS_CurveH	'Pump Curve'!$B$11:$B$22
DWS_CurveP	'Pump Curve'!$C$11:$C$22
DWS_CurveQ	'Pump Curve'!$A$11:$A$22
DWS_EffBEP	'Pump Curve'!$B$26
DWS_EffOp	Calc!$B$25
DWS_F	Calc!$B$19
DWS_FTarget	Calc!$B$18
DWS_Fbase	Inputs!$B$20
DWS_FlowID	Inputs!$B$15
DWS_FlowL	Inputs!$B$16
DWS_FreqSet	Inputs!$B$21
DWS_Grad	Calc!$B$6
DWS_GridTop	Calc!$B$21
DWS_HInj	Calc!$B$10
DWS_HSink	Calc!$B$9
DWS_HStgT	Calc!$B$15
DWS_HfT	Calc!$B$11
DWS_Hst	Calc!$B$8
DWS_HstFlag	Calc!$B$29
DWS_II	Inputs!$B$12
DWS_Kq	Calc!$B$14
DWS_MotorHP	Inputs!$B$25
DWS_MotorOD	Inputs!$B$27
DWS_N	Calc!$B$17
DWS_PI	Inputs!$B$10
DWS_PackerRating	Inputs!$B$31
DWS_Pdr	Inputs!$B$9
DWS_Pinj	Inputs!$B$11
DWS_PinjSt	Calc!$B$7
DWS_PumpModel	'Pump Curve'!$B$5
DWS_Q	Inputs!$B$5
DWS_QBEP	'Pump Curve'!$B$25
DWS_Qd	Calc!$B$5
DWS_Qmax	'Pump Curve'!$B$7
DWS_Qmin	'Pump Curve'!$B$6
DWS_Qop	Calc!$B$22
DWS_R	Calc!$B$20
DWS_SF	Inputs!$B$26
DWS_SG	Inputs!$B$7
DWS_SGFlag	Calc!$B$28
DWS_Shaft	Inputs!$B$30
DWS_Sink	Inputs!$B$6
DWS_SinkOp	Calc!$B$27
DWS_SinkShare	Calc!$B$26
DWS_StagesReq	Calc!$B$16
DWS_StagesSet	Inputs!$B$22
DWS_TDH	Calc!$B$13
DWS_TDHKnown	Inputs!$B$17
DWS_TDHLoop	Calc!$B$12
DWS_TDHop	Calc!$B$23
DWS_Temp	Inputs!$B$29
DWS_VsdF	Inputs!$B$35:$H$35
DWS_dZ	Inputs!$B$13

Opens in	Needs the Petroleum Office add-in: its PO functions show #NAME? without it once Excel recalculates.
Functions used	PO.ESP.Curve.BEP PO.ESP.Curve.BEP.Eff PO.ESP.Curve.Efficiency PO.ESP.Curve.Head PO.ESP.Curve.InRange PO.ESP.Curve.Power PO.ESP.Head.FromPressure PO.ESP.Head.ToPressure PO.ESP.HydraulicHP PO.ESP.Motor.Load.Status PO.ESP.Motor.LoadFactor PO.ESP.Motor.RequiredHP PO.ESP.Motor.Temp.Rise PO.ESP.Nodal.Drawdown PO.ESP.Pump.Efficiency PO.ESP.Pump.TotalHead PO.ESP.Stages PO.ESP.Stages.Actual PO.ESP.System.Hfric
File	DwsInvertedEspSizing.xlsx, 62 KB
Category	Production
For agents and tools	Structure (.json) · Descriptor (.md)

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Tags:

espdownhole-water-sinkdownhole-water-loopinverted-espwater-injectionpump-sizingperformance-curvevsdaffinity-laws