Login| Sign Up| Help| Contact|

Patent Searching and Data


Title:
ELECTRIC SUBMERSIBLE PUMP MONITORING
Document Type and Number:
WIPO Patent Application WO/2016/205101
Kind Code:
A1
Abstract:
Systems and methods for monitoring an electric submersible pump include measuring voltage and current of a power output of a multi-phase power drive configured to power a downhole motor to thereby produce measured voltage and current values. The method also includes estimating the voltage of the downhole motor for each of multiple phases based on the measured voltage and current values, extracting positive and negative sequence voltage and current from the estimated voltage of the downhole motor and from the measured current value, estimating a differential pressure across a downhole pump powered by the downhole motor based on the extracted positive and negative sequence voltage and current, and adjusting operation of the downhole motor based on the estimated differential pressure across the pump.

Inventors:
DASGUPTA, Souvik (#12-140, Block 102 Jurong East 13, Singapore 2, 600102, SG)
RENDUSARA, Dudi Abdullah (6 Cedarwood Grove, Woodlands 4, 738424, SG)
KANDASAMY, Sakthivel (7 Benoi Crescent, Singapore 1, 629971, SG)
MAHADEVAN, Pradeep (7 Benoi Crescent, Singapore 1, 629971, SG)
Application Number:
US2016/037144
Publication Date:
December 22, 2016
Filing Date:
June 13, 2016
Export Citation:
Click for automatic bibliography generation   Help
Assignee:
SCHLUMBERGER TECHNOLOGY CORPORATION (300 Schlumberger Drive, Sugar Land, Texas, 77478, US)
SCHLUMBERGER CANADA LIMITED (125 - 9 Avenue SE, Calgary, Alberta T2G 0P6, 0P6, CA)
SERVICES PETROLIERS SCHLUMBERGER (42 rue Saint Dominique, Paris, Paris, FR)
SCHLUMBERGER TECHNOLOGY B.V. (Parkstraat 83-89m, JG The Hague, Hague, NL)
International Classes:
F04B49/06; E21B43/12; F04B47/06
Foreign References:
US20040062657A12004-04-01
US20100155057A12010-06-24
US20150083399A12015-03-26
US20130175030A12013-07-11
US20070263331A12007-11-15
Attorney, Agent or Firm:
STONEBROOK, Michael et al. (10001 Richmond Avenue, IP Administration Center of ExcellenceRoom 472, Houston Texas, 77042, US)
Download PDF:
Claims:
CLAIMS

lat is claimed is:

A method, comprising:

measuring voltage and current of a power output of a multi-phase power drive configured to power a downhole motor to thereby produce measured voltage and current values;

based on the measured voltage and current values, estimating the voltage of the downhole motor for each of multiple phases;

extracting positive and negative sequence voltage and current from the estimated voltage of the downhole motor and from the measured current value;

estimating a differential pressure across a downhole pump powered by the downhole motor based on the extracted positive and negative sequence voltage and current; and adjusting operation of the downhole motor based on the estimated differential pressure across the pump.

The method of claim 1 wherein estimating the differential pressure comprises:

computing a torque value based on the extracted positive and negative sequence voltage and current; and

determining an estimate of the differential pressure based on the computed torque, a specific gravity of pumped fluid, and an estimate of motor speed.

The method of claim 2 further comprising computing an output power of the motor based the computed torque value and the estimate of motor speed.

4. The method of claim 2 wherein computing the torque value comprises:

computing a direct current (DC) torque based on the extracted positive sequence voltage and current;

computing a DC torque based on the extracted negative sequence voltage and current; and summing the computed DC torques based on the extracted positive and negative sequence voltage and currents to produce a total electromagnetic DC torque.

5. The method of claim 4 further comprising subtracting a viscosity drag force from the total electromagnetic DC torque to compute the torque value.

6. The method of claim 1 further comprising estimating an expected healthy differential pressure across the pump based on the estimated voltage of the downhole motor, the measured current value, and an average specific gravity of pump fluid during a time interval proximate to the estimation of the healthy pump pressure head.

7. The method of claim 6 further comprising:

computing a fault indicator based on the difference between an actual differential pressure across the pump and the estimated expected healthy differential pressure across the pump; and

adjusting operation of the downhole motor based on the fault indicator.

8. A non-transitory storage device contains software that, when executed by a processing resource, causes the processing resource to perform the method of claim 1.

9. A motor monitor processing system comprising:

a storage device storing executable code; and

a processing resource coupled to the storage device configured to execute the executable code to perform the method of claim 1.

10. A method, comprising:

measuring voltage and current of a power output of a multi-phase power drive configured to power a downhole motor to thereby produce measured voltage and current values;

based on the measured voltage and current values, estimating the voltage of the downhole motor for each of multiple phases;

extracting positive, negative, and zero sequence voltage and current from the estimated voltage of the downhole motor and from the measured current value; determining positive, negative, and zero sequence impedances based on the positive, negative, and zero sequence voltages and currents, respectively, to thereby produce a complex sequence impedance pair; and

adjusting operation of the downhole motor based on the complex sequence impedance pair.

11. The method of claim 10 further comprising identifying an electrical fault type or location based on the complex sequence impedance pair.

12. The method of claim 11 further comprising comparing the complex sequence impedance pair to a database of experimentally-determined impedance pairs indicating one or more electrical fault types or one or more electrical fault locations.

13. The method of claim 10 further comprising:

determining a baseline sequence impedance pair when a pump driven by the motor is in a known, healthy state; and

adjusting operation of the downhole motor when a subsequent sequence impedance pair deviates from the baseline sequence impedance pair by more than a predetermined amount.

14. A non-transitory storage device contains software that, when executed by a processing resource, causes the processing resource to perform the method of claim 10.

15. A motor monitor processing system comprising:

a storage device storing executable code; and

a processing resource coupled to the storage device configured to execute the executable code to perform the method of claim 10.

16. A method, comprising:

measuring voltage and current of a power output of a multi-phase power drive configured to power a downhole motor to thereby produce measured voltage and current values;

based on the measured voltage and current values, estimating the voltage of the downhole motor for each of multiple phases;

extracting positive sequence voltage and current from the estimated voltage of the downhole motor and from the measured current value;

determining positive sequence impedance at terminals of the motor based on the positive sequence voltage and current; and

adjusting operation of the downhole motor based on the positive sequence motor terminal impedance.

17. The method of claim 16 further comprising:

determining a baseline positive sequence motor terminal impedance value when a pump driven by the motor is in a known, healthy state; and

adjusting operation of the downhole motor when a subsequent positive sequence motor terminal impedance value deviates from the baseline positive sequence motor terminal impedance value by more than a predetermined amount.

18. The method of claim 16 further comprising adjusting operation of the downhole motor when the positive sequence motor terminal impedance value decreases below a predetermined threshold value.

19. A non-transitory storage device contains software that, when executed by a processing resource, causes the processing resource to perform the method of claim 16.

A motor monitor processing system comprising:

a storage device storing executable code; and

a processing resource coupled to the storage device configured to execute the executable code to perform the method of claim 16.

Description:
ELECTRIC SUBMERSIBLE PUMP MONITORING CROSS-REFERENCE TO RELATED APPLICATIONS [0001] The present application claims priority to U.S. Provisional Application No. 62/180,291 filed June 16, 2015, entitled "Estimation of ESP Motor Shaft Torque," which is incorporated herein by reference in its entirety for all purposes.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] Not applicable.

BACKGROUND

[0003] Some oil and gas production rigs employ an artificial lift electrical submersible pump (ESP) to increase pressure within a reservoir to thereby encourage oil to the surface. When the natural drive energy of the reservoir is not sufficient to push the oil to the surface, artificial lift is employed to recover more production. An artificial lift system often includes an electric submersible pump (ESP) driven by an induction motor. The ESP, including the induction motor, is placed downhole and the motor is driven by an electric current produced by surface power equipment.

[0004] Downhole ESPs and their motors operate in harsh environments and may fail over time. Even if such equipment does not completely fail, the performance of the motor and ESP may be impaired due to, for example, mechanical wear or failure caused by bearing wear, impeller wear, and the like, as well as electrical failures such as a short circuit at the motor lead extension (MLE). If such problems are not detected quickly, there can be a catastrophic mechanical or electrical failure of the ESP system. Some operators simply wait for the ESP and/or motor to completely fail before retrieving the equipment to the surface and replacing it.

SUMMARY

[0005] Various performance parameters associated with a downhole induction motor and electric submersible pump are determined based on surface measurements of current and voltage, measurements of physical properties of vibration, other measurements, and combinations thereof.

[0006] Certain systems and methods of the present disclosure for monitoring an electric submersible pump include measuring voltage and current of a power output of a multi-phase power drive configured to power a downhole motor to thereby produce measured voltage and current values. The systems and methods also include estimating the voltage of the downhole motor for each of multiple phases based on the measured voltage and current values, extracting positive and negative sequence voltage and current from the estimated voltage of the downhole motor and from the measured current value, estimating a differential pressure across a downhole pump powered by the downhole motor based on the extracted positive and negative sequence voltage and current, and adjusting operation of the downhole motor based on the estimated differential pressure across the pump.

[0007] Certain other systems and methods of the present disclosure for monitoring an electric submersible pump include measuring voltage and current of a power output of a multi-phase power drive configured to power a downhole motor to thereby produce measured voltage and current values. The systems and methods also include estimating the voltage of the downhole motor for each of multiple phases based on the measured voltage and current values; extracting positive, negative, and zero sequence voltage and current from the estimated voltage of the downhole motor and from the measured current value; determining positive, negative, and zero sequence impedances based on the positive, negative, and zero sequence voltages and currents, respectively, to thereby produce a complex sequence impedance pair; and adjusting operation of the downhole motor based on the complex sequence impedance pair.

[0008] Yet other systems and methods of the present disclosure for monitoring an electric submersible pump include measuring voltage and current of a power output of a multi-phase power drive configured to power a downhole motor to thereby produce measured voltage and current values. The systems and methods also include estimating the voltage of the downhole motor for each of multiple phases based on the measured voltage and current values, extracting positive sequence voltage and current from the estimated voltage of the downhole motor and from the measured current value, determining positive sequence impedance at terminals of the motor based on the positive sequence voltage and current, and adjusting operation of the downhole motor based on the positive sequence motor terminal impedance.

[0009] In some embodiments, a non-transitory storage device contains instructions or software that, when executed by a processing resource, causes the processing resource to perform portions or all of the various methods described herein.

[0010] This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Embodiments of the disclosure are described with reference to the following figures:

[0012] FIG. 1 illustrates an electric submersible pump including an induction motor and an associated control and monitoring system deployed in a wellbore environment in accordance with various embodiments of the present disclosure;

[0013] FIG. 2 shows an example of an induction motor including multiple radial bearings in accordance with various embodiments of the present disclosure;

[0014] FIG. 3 shows an example of a method for estimating differential pressure across a pump driven by an induction motor used down-hole in accordance with various embodiments of the present disclosure;

[0015] FIG. 4 shows an example of an approximately equivalent circuit model of the motor described herein in accordance with various embodiments of the present disclosure;

[0016] FIG. 5 shows a technique for computing total DC torque from torques computed from positive and negative sequences of the present disclosure;

[0017] FIG. 6 shows an example of a method for identifying faults in an electric submersible pump (ESP) electrical system in accordance with various embodiments of the present disclosure;

[0018] FIG. 7 shows an example of a trending fault indicator over time in accordance with various embodiments of the present disclosure;

[0019] FIG. 8 shows an example cross-sectional view of a motor stator and rotor with exemplary orbital shaft motion in accordance with various embodiments of the present disclosure;

[0020] FIG. 9 shows an alternate example of a trending fault indicator over time in accordance with various embodiments of the present disclosure; [0021] FIG. 10 shows a cross-sectional view of a motor in accordance with various embodiments of the present disclosure;

[0022] FIG. 11 shows an exemplary frequency plot of induced flux in accordance with various embodiments of the present disclosure;

[0023] FIG. 12 shows an example block diagram of a system for pump health assessment in accordance with various embodiments of the present disclosure;

[0024] FIG. 13 shows a system diagram of a motor monitor processing system in accordance with various embodiments of the present disclosure;

[0025] FIG. 14 shows an exemplary frequency response plot in accordance with various embodiments of the present disclosure; and

[0026] FIG. 15 shows exemplary vibration-based health indicators over time in accordance with various embodiments of the present disclosure.

DETAILED DESCRIPTION

[0027] One or more embodiments of the present disclosure are described below. These embodiments are merely examples of the presently disclosed techniques. Additionally, in an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such implementation, as in any engineering or design project, numerous implementation-specific decisions are made to achieve the developers' specific goals, such as compliance with system- related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such development efforts might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.

[0028] When introducing elements of various embodiments of the present disclosure, the articles "a," "an," and "the" are intended to mean that there are one or more of the elements. The embodiments discussed below are intended to be examples that are illustrative in nature and should not be construed to mean that the specific embodiments described herein are necessarily preferential in nature. Additionally, it should be understood that references to "one embodiment" or "an embodiment" within the present disclosure are not to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. The drawing figures are not necessarily to scale. Certain features and components disclosed herein may be shown exaggerated in scale or in somewhat schematic form, and some details of conventional elements may not be shown in the interest of clarity and conciseness.

[0029] References to "based on" should be interpreted as "based at least on." For example, if the calculation of parameter X is "based on" value Y, then the calculation of X is based at least on the value of Y; the calculation of X may be based on other values as well.

[0030] The terms "including" and "comprising" are used herein, including in the claims, in an open-ended fashion, and thus should be interpreted to mean "including, but not limited to... ." Also, the term "couple" or "couples" is intended to mean either an indirect or direct connection. Thus, if a first component couples or is coupled to a second component, the connection between the components may be through a direct engagement of the two components, or through an indirect connection that is accomplished via other intermediate components, devices and/or connections. If the connection transfers electrical power or signals, the coupling may be through wires or other modes of transmission. In some of the figures, one or more components or aspects of a component may be not displayed or may not have reference numerals identifying the features or components that are identified elsewhere in order to improve clarity and conciseness of the figure.

[0031] Electric submersible pumps (ESPs) may be deployed for any of a variety of pumping purposes. For example, where a substance does not readily flow responsive to existing natural forces, an ESP may be implemented to artificially lift the substance. Commercially available ESPs (such as the RED A™ ESPs marketed by Schlumberger Limited, Houston, Tex.) may find use in applications that require, for example, pump rates in excess of 4,000 barrels per day and lift of 12,000 feet or more.

[0032] As explained above, ESPs operated down-hole may experience any of a variety of failures due at least in part to the harsh environments in which the ESPs operate. An ESP may include a pump that is driven by an electric induction motor. A symptom of a failure or a potential future failure of a pump or motor is a change in differential pressure across the pump of the ESP such that the differential pressure is outside an expected range of normal values. For example, a lower-than-expected pump differential pressure may indicate a no-flow or an unacceptably low- flow condition, which may impair pump performance. For various ESP systems, an estimation of pump differential pressure may be useful in predicting ESP health or degradation thereto. In order to estimate pump differential pressure, motor shaft output power is an important variable, which is determined based on motor output torque and motor speed. However, it is often not feasible to utilize downhole torque and speed sensors to determine those values.

[0033] The disclosed embodiments include a processing system provided at the surface that analyzes an electric signal of the induction motor and, from that signal, estimates a motor output torque and power. In some embodiments, the current and voltage at the surface to be provided to the downhole motor are measured. The terminal voltage of the downhole motor is estimated based on the surface measurement of current and voltage. The estimated motor terminal voltage and the current are further processed to extract positive sequence voltage and current and, from the positive sequence values, the motor output torque is estimated. To estimate differential pressure across a pump of the ESP, motor output torque is estimated based on extracted positive and negative sequences of current and voltage. Motor speed also can be estimated and, with the estimated torque, used to compute motor output power. The motor output power corresponds to the pump input power, while the motor speed corresponds to the pump speed. Differential pressure across the pump can be estimated based on the estimates of pump input power and pump speed. Differential pressure across the pump and other variables may then can be compared to their normal operating ranges or an expected range of normal values and corrective actions (e.g., turning off the motor and pump) can be taken upon detecting a deviation from the normal range.

[0034] FIG. 1 depicts one example of a completion 10 within a well bore 12. The completion 10 incorporates an electric submersible pump (ESP) 24. There are many examples of possible well completion architectures which incorporate various other downhole tools such as packers, by-pass tubing, and ESP encapsulation, which are a few such tools. The presently disclosed systems and methods are independent of the completion architecture used in the specific application outside of the use of an ESP. While the systems and methods disclosed herein may be focused on hydrocarbon wells, it is understood that these and other embodiments may be used for any type of liquid being pumped with an ESP. Non-limiting examples include: hydrocarbons from an oil well, water from a water well, water from a geothermal well, water from a gas well, hydrocarbons from a sump, and so on. In the case of an oil well, an ESP 24 may be deployed in the completion 10 in order to improve production of hydrocarbons. [0035] The ESP 24 includes a motor 26 and a pump 30. The motor 26 may be housed within the same housing as the pump 30, or may be housed separately. The motor 26 operates to drive the pump 30 in order to increase hydrocarbon production to the surface. The ESP 24 further includes an intake pressure gauge 32 which measures the pressure upstream of the ESP 24. The ESP 24 further includes a discharge pressure gauge 34 which measures the pressure downstream of the ESP 24.

[0036] The motor 26 of the ESP 24 receives electrical energization from a switch gear such as a variable speed drive (VSD) 90 typically located at the surface, outside of the well completion. The VSD 90 controls the power to, and thus the speed of, the motor 26. The VSD 90 may be driven by a three-phase power source and thus may be a multi-phase power drive. The VSD 90 delivers energization to the ESP 24 through an electrical conduit 38. A digital acquisition system 95 also is included that receives an electrical signal of the VSD 90 and digitizes the signal. The signal may include measurements of voltage and current for each of multiple phases 92. The digital acquisition system 95 may include one or more analog-to-digital converts (DACs) to convert analog VSD signals to digital form. The digitized signals are then provided to a motor monitor processing system 100 for the computation of estimates of motor shaft output torque, motor output power, and pump differential pressure.

[0037] The motor monitor processing system 100 thus receives the digitized surface current and voltage measurement and processes them to estimate the pump differential pressure as is explained in detail below. An alert 101 may be generated by the motor monitor processing system 100 to announce the detection of a problem (e.g., pump differential pressure or another variable being outside a corresponding nominal range). The motor monitor processing system 100 alternatively or additionally may generate a feedback signal 103 to be provided to the VSD 90 to change the operation of the motor 26 (e.g., reduce the speed of the motor, turn the motor off, etc.).

[0038] The motor 26 may be implemented as an induction motor (and thus may also be referred to as induction motor 26). FIG. 2 shows a schematic of one example of induction motor 26. In this example, induction motor 26 includes four radial bearings 32, 34, 36, and 38 and three rotor segments 40, 42, and 44. The rotor segments 40-44 are arranged sequentially along their longitudinal axes. A radial bearing (34, 36) is provided between each pair of adjacent rotor segments, and a radial bearing (32, 38) is provided at each end of the longitudinally-arranged rotor segments 40-44. Any number of rotor segments and radial bearings can be provided other than what is shown in the example of FIG. 2. On opposing ends of each rotor segment are rotor end rings. Thus, rotor segment 40 includes end rings 50 and 52. Rotor segment 42 includes end rings 54 and 56. Rotor segment 44 includes end rings 58 and 60. A shaft 62 is provided through the center of the rotor segments 40-44. As the rotor segments are caused to turn, the shaft 62 also turns. The speed at which the shaft 62 turns is referred to as the rotor shaft speed, shaft speed, and/or motor speed. Shaft speed may be expressed in units of revolutions per unit of time (e.g. , revolutions per second). The rotor segments 40-44 and radial bearings 32-38 are contained within a generally cylindrical stator 30. Alternating magnetic fields in the stator 30, caused by current from the VSD 90, cause the rotor segments 40-44 to turn.

[0039] FIG. 3 shows an example of a method for estimating a downhole induction motor's output torque, power, and a corresponding pump differential pressure in accordance with embodiments of the present disclosure. The operations can be performed in the order shown, or in a different order. Further, two more of the operations may be performed concurrently rather than sequentially. At 102, the method includes measuring the voltage and current at the surface. In some embodiments, the electrical power to operate the downhole motor and pump is a 3-phase supply and thus, at 102, the voltage and current of each of the three phases is measured. For example, the output voltage and current of the VSD 90 is measured and digitized by the digital acquisition system 95. A low resistance resistor may be provided on each of the three phase conductors and the voltage across the resistor is monitored and used as a proxy for the current of that phase. The digitized measurements of current and voltage may be provided to the motor monitor processing system 100 which performs some or all of the rest of the operations of FIG. 3.

[0040] At 104, the method includes estimating the motor's terminal voltage, that is, the voltage at the input terminals of the motor itself, which may be connected through lengthy (dozens, hundreds, or thousands of feet) cables to the VSD 90. The estimate of motor terminal voltage may be based on the surface measured voltage as well as the surface measured current. As the motor may be located hundreds or thousands of feet downhole, due to the impedance of the electrical cables themselves that transfer power to the motor, the voltage at the motor will generally be less than the voltage at the surface. Using, for example, a simplified power frequency cable model, the motor terminal voltages for all three phases may be determined as: vm,x (t) = v s,x (t (Rcable,x)ix (f) cable, x ~^~ ) where "m" refers to the motor, "x" refers to the phase {e.g., phase a, phase b, phase c), "s" refers to the surface {i.e., v s x {t) is the voltage measured at the surface for each phase with respect to time), Rcabie,x and L ca bie,x refer to the resistance and inductance of a cable of each phase from the surface to the motor, and is the derivative of current of each phase with respect to time. One implementation of equation (1) above is provided below: vm,x(.k) = v s,xQl) (Rcai)ie,x)^ (^) {L cable x ) ** " ^ ^ - (2) where "k" is an index value to a given voltage sample and Ts refers to the sampling interval. [0041] The estimated voltage at the motor's terminal as well as the currents may be unbalanced due to electrical asymmetry in the system such as cable asymmetry, motor lead extension (MLE) asymmetry, etc. As such, the illustrative embodiment of FIG. 3 for estimating motor output torque based on estimates of motor terminal voltage may be performed by extracting the positive and negative sequence voltages and currents (operation 106 in FIG. 3). Considering a three-phase system, symmetrical components (positive sequence, negative sequence, and zero sequence) permit analysis of power system operations during unbalanced conditions such as those caused by faults between phases and/or ground, open phases, unbalanced impedances, and so on. The positive sequence set includes the balanced three-phase currents and line-to-neutral voltages provided by the VSD 90. The positive sequence set is equal in magnitude and phase displaced by 120 degrees rotating at the system frequency with a phase sequence of normally a, b, c. The negative sequence set is also balanced with three equal magnitude quantities at 120 degrees apart but with the phase rotation or sequence reversed, or a, c, b. The members of the zero-sequence set of rotating phasors are equal in magnitude and are in phase.

[0042] Any suitable technique to extract the positive and negative sequence component can be performed by the motor monitor processing system 100 in operation 106. For example, in some embodiments, the positive sequence component can be extracted as follows. The estimated/calculated three phase motor terminal voltages and currents can be processed by a narrow bandpass filter to recover the content at the fundamental frequency. The narrow bandpass filter may be tuned to the fundamental frequency detected in the estimated motor terminal voltage and current. The narrow bandpass filter may be tuned to the fundamental frequency through a feedback signal generated by the combination of a zero crossing detector and adaptive tuner. Additionally or alternatively, a phase-lock loop (PLL) may be used to provide an estimate of the fundamental frequency.

[0043] The motor monitor processing system 100 then extracts the positive sequence components from the filtered motor terminal voltages and currents. The motor monitor processing system 100 also may extract the negative and/or zero sequence components. Any of a variety of techniques can be employed to extract the sequence components. For example, the sequence components of voltages and currents can be estimated using Fortescue's method. Per that method,

Xap i = [x a (f) + 5(120° ( + 5( 120°)x c (t)] (3) x aN (t = \ [x a (t) + 5( 120°)¾(t) + S(120°)* c (t)] (4)

*αθ( = [Xa (t) + x b (t) + X c (t)] (5) where "S" is a phase shifter operator (e.g., S(120 )x(t) refers to shifting the phase of x(t) by 120 degrees in a positive direction and S(-120°)x(t) refers to shifting the phase of x(t) by 120 degrees in a negative direction). The variable "x" in the above three equations refers to motor voltage or current. Thus, "xap(t)" refers to the positive sequence component for current/voltage for phase a. Similarly, "xaN(t)" refers to the negative sequence component for current/voltage for phase a and "xao(t)" refers to the zero sequence component for current/voltage for phase a.

[0044] Many filtering techniques can be used to perform operations of equations (3)-(5). One such example is to use a phase shifting all-pass filter such as:

¾P F O) = le- 2 tan- i (a/r 3)

(7) This type of filter introduces 120° phase shift at frequency ω = ^ rad/s, thereby implementing the S ( 120°) operator. Thus, the phase shifting operators can be implemented using the following equations:

S( 120°) « le-JZ tan-Hwr s) (8) 5(120°) = -l-5( 120°) (9)

In real-time or near real-time, the implementation can be performed using the following digital equations: y (k = \^ ] ^ )* (fc) + x(fc ^ + ^ i)] do)

Once the phase "a" positive sequence component for voltage and current is computed, the corresponding positive sequence voltages and currents can be calculated by shifting the phase "a" sequence components +/- 120°.

[0045] At 108 in the example of FIG. 3, the method includes computing the electromagnetic DC torque for the positive sequence voltage and current and separately (110) for the negative sequence voltage and current. At least some of these techniques may be based on the approximate steady state equivalent circuit of the motor 26 as shown in the example of FIG. 4. The resistance RM represents the core-loss resistance. The resistance r s represents the stator resistance and is in series with the mutual inductance lh multiplied by a stator stray factor a s , as well as lh multiplied by a rotor stray factor σ Γ and the rotor resistance r r divided by the rotor slip, S. The mutual inductance lh is also provided as shown. These values can be computed through known techniques such as through use of an analytical, semi-empirical motor model, which uses as inputs motor winding code information, stator temperature information, and operating condition information (e.g., root mean square voltage and approximate horsepower). The model outputs the various inductances, resistances, and factors. FIG. 5 illustrates an example of the computation of electromagnetic DC torque. To compute the DC torque for the positive voltage sequence Vf P and current sequence If P , a motor stator induced electromotive force (emf) vector E sP is calculated at 280 based on the positive voltage and current sequence (at the fundamental frequency), as well as the motor per phase core-loss resistance (RM) and the motor per phase stator resistance (r s ). The emf vector E sP may be computed as:

At 282, the dot product of E sP and an interim current vector II is computed. The interim current vector II may be computed as:

Tl = If P (12)

The dot vector operation is computed by multiplying corresponding elements of the E sP and the

II vectors and summing the products together to generate an electromagnetic DC torque value for the positive sequence current and voltage. Similar calculations are performed for the negative current and voltage sequences at 290 and 292 to generate an electromagnetic DC torque value for the negative sequence current and voltage. The two electromagnetic DC torques (for the positive and negative voltage and current sequences) are then added together at 112 in FIG. 3 (as also illustrated at 295 in FIG. 5) to compute the total electromagnetic DC torque.

[0046] Referring back to FIG. 3, at 114 the method may comprise subtracting a viscosity drag force from the total electromagnetic DC torque to compute the DC torque generated by the motor. Any of a variety of techniques can be employed to determine a viscosity drag force. In one example, an oil drag force /viscosity model may be generated apriori for the particular motor being used, such as through empirical analysis. This model may also factor in a friction load value from the bearings. Inputs to such a model may include motor speed as determined by, for example, MCSA, oil temperature, and oil pressure.

[0047] At 116, the motor speed is estimated (and may have been estimated and used in operation 114 to compute a viscosity drag force) and used at 118 to compute the output power from the motor, and thus the input power to the pump driven by the motor. The motor's output power may be computed as the total electromagnetic DC torque computed at 114 multiplied by the motor speed.

[0048] Certain embodiments of the present disclosure may leverage the motor's output power and the motor speed to determine flow rate through the pump. For example, empirical studies can be performed on the pump (having a known number of pump stages) to measure flow rates for a known liquid (i.e., a liquid (e.g., water) with a known specific gravity), at a fixed reference speed, but at varying power levels for the pump. From such data, flow rate coefficients of a polynomial can be generated, and will be application specific based on the particular pump being tested. The variable in the polynomial may itself be a function of pump input power, pump speed, and the specific gravity of whatever fluid is being pumped, which may be measured or determined contemporaneously with the calculation of the pump differential pressure. In one example, the variable (X) to be input into the polynomial can be calculated as:

where "power" is the output power from the motor as calculated above based on DC torque (and thus the input power to the pump) and motor speed, "num" is the number of stages of the pump, "SPG" is the average specific gravity of the particular fluid being pumped over a sampling interval, "co" is the estimated motor (and thus pump) speed as determined by, for example, motor current signature analysis ("MCSA"), and "core/' is the reference speed of the motor during the empirical analysis explained above. The variable X is in effect normalized to, for example, a single pump stage, pumping water, at the reference speed. Subsequently then, the polynomial is evaluated based on the calculated value of X to produce an estimate of the flow rate of the fluid being pumped. The experimentally-determined flow rate coefficients are applicable since X has been normalized to the same conditions used to determine those coefficients.

[0049] However, in certain cases knowledge of the flow rate through the pump, without more, may be insufficient to accurately determine or predict an indication of the pump's current health. For example, in the event of gas lock or a high mud condition, flow rate may be affected due to the well fluid condition without any pump health issues existing. To address some of the issues with flow rate-based assessments, certain embodiments of the present disclosure leverage a comparison of a healthy expected differential pressure across the pump with an actual differential pressure across the pump to determine a pump health indicator.

[0050] Thus, at 120, the method includes determining or computing a healthy expected differential pressure across the pump. In accordance with various embodiments, the motor's output power (which also represents the input power to the pump 30) and the motor speed (which also represents the pump's speed) are used, at least in part, to determine the flow rate through the pump as explained above. The determined flow rate may then be leveraged to compute the healthy expected differential pressure across the pump. As above, empirical studies can be performed on the pump (with a known number of pump stages) to measure differential pressures across the pump for a known liquid (i. e. , a liquid (e.g. , water) with a known average specific gravity over a sampling interval), at a fixed reference speed, but at varying power levels for the pump. From such data, various pump performance curves may be generated, which in turn may be used to generate differential pressure coefficients of a polynomial, which will be application specific based on the particular pump being tested. The variable in the polynomial to determine differential pressure is the flow rate itself, as determined above.

[0051] However, although the flow rate may be calculated in a normalized manner (i. e. , the flow rate through one stage will be the same as the flow rate through all pump stages), the differential pressure calculated from that flow rate will be across only one stage, and at a reference speed, and is thus referred to as a normalized differential pressure. To determine the actual differential pressure (i.e., the healthy expected differential pressure across all pump stages), the normalized differential pressure is multiplied by the number of pump stages and the quantity I -^— ) .

[0052] Once the healthy expected differential pressure is computed at 120, the method includes calculating a fault indicator, which is based on the healthy expected differential pressure and the actual differential pressure across the pump. FIG. 6 shows an example of a trending fault indicator F.I. over time. The estimated healthy differential pressure across the pump, P est , is determined using any of the above-described approaches. The actual differential pressure across the pump, P ac , may be determined from downhole data received from one or more gauges 32, 34. In certain embodiments then, the fault indicator is given by:

F. I. = P est P ac (14)

[0053] At 124, the method includes determining whether the fault indicator exceeds a threshold or deviates from an expected range of values. For example, during a first period of time 602 in which the fault indicator is determined, the fault indicator remains relatively level, which means the difference between estimated healthy differential pressure and actual differential pressure is unchanging, and thus that the pump is operating in a healthy manner. Note that it is not necessary that the difference in actual and estimated healthy differential pressure be zero in order to indicate that the pump operation is healthy. Rather, in certain cases, a threshold (shown in FIG. 6) of maximum allowed difference - or fault indicator value - may be determined and utilized for pump health monitoring. During the time period 604, the difference between actual and estimated healthy differential pressure is increasing, but still below the threshold of maximum allowed difference. In certain embodiments, such deviations from an approximate flatline fault indicator value may be displayed or otherwise conveyed to an operator, even though the fault indicator remains below the threshold. However, when the fault indicator exceeds the threshold during the time period 606 - that is, the difference between actual and estimated healthy pressure head exceeds the threshold - a warning is generated and corrective action (e.g., shutting off the pump) may be taken, as shown at 126 of the method in FIG. 3.

[0054] Of course, although the method of FIG. 3 generally relates to differential pressure-based analysis, embodiments of the present disclosure may also be directed to a flow rate-based analysis. For example, where the flow rate (as calculated above) is below a predetermined threshold, indicating a no- or low-flow condition at the pump, the step of 126 may also follow. That is, a warning is generated and corrective action (e.g., shutting off the pump) may be taken when the calculated flow rate is below the predetermined threshold.

[0055] In addition to determining a fault indicator based on expected healthy and actual measured differential pressure across the ESP pump, for example to take corrective action to prolong a lifespan of the pump, some embodiments of the present disclosure are directed to detecting electrical faults that cause unbalanced conditions in the ESP power system, such as those caused by faults between phases and/or ground, open phases, unbalanced impedances, and so on. Referring back to FIG. 1, the phase impedances in the cables between the surface and the motor are typically asymmetrical, and embodiments are directed to detecting electrical faults through analysis of the sequence impedances in the ESP system. [0056] As explained above, it is possible to extract positive, negative, and zero sequence components of voltage and current. To compute the sequence impedances, the sequence voltages are divided by the respective sequence currents as follows:

Ζ Ρ =ψ (15) Ζ Ν = ψ (16)

where Zp, ZN, and Zo are the instantaneous positive, negative, and zero sequence complex impedances, respectively, which may be computed in real-time. Embodiments of the present disclosure utilize an ESP signature that is based on the complex sequence impedance pair given

[0057] Turning now to FIG. 7, a method is illustrated to identify a fault using the complex sequence impedance pair {Zp, ZN, ZO} derived above. Prior to performing the method shown in FIG. 7, one or more synthetic fault-experiments may be performed on a particular ESP electrical system. The synthetic experiments may simulate a variety of different types of faults, such as an inter-phase fault, a phase-to-ground fault, an inter-turn fault, and the like. Similarly, the synthetic experiments may simulate the faults in a variety of locations, such as in the cable, at the motor lead extensions, at a tandem connection, a lower tandem (LT), center tandem (CT), or upper tandem (UT) motor, and the like. A sequence impedance pair {Zp, ZN, ZO} is calculated for each synthetic fault-experiment, resulting in a database or databank of sequence impedance pairs associated with different types and/or locations of faults that may occur on the ESP electrical system. In some cases, the database may be populated with synthetic fault-experiment sequence impedance pairs using a model of the ESP electrical systems including the fault, while in other cases the database may be populated by causing faults on the actual ESP electrical system.

[0058] Similar to the method of FIG. 3 explained above, the method shown in FIG. 7 begins at 702 with measuring voltage and current for each phase at the surface and continues at 704 with estimating motor terminal voltage and current based on the measured surface values. At 706, positive, negative, and zero sequence voltages and currents are extracted, again as described above. At 708, the positive, negative, and zero sequence impedances are computed (e.g., as shown in equations 15-17), resulting in a complex sequence impedance pair {Zp, ZN, ZO} . The computed sequence impedance pair {Zp, ZN, ZO} may be compared to the database or databank of sequence impedance pairs described above to ascertain whether the computed sequence impedance pair matches (or is within a threshold or range relative to) one or more of the experimentally- determined sequence pairs associated with different types and/or locations of faults that may occur on the ESP electrical system.

[0059] The identification algorithm that determines a match may be an adaptive learning algorithm such as neural network-based, iterative learning-based, and the like. If a match is found with, or if the computed sequence impedance pair is within less than a threshold amount of, one of the experimentally-determined sequence pairs indicating a fault, that fault is identified at 710. Further, in certain cases, an initial sequence impedance pair may be identified for the ESP electrical system in a known healthy state. Then, subsequent deviations in computed sequence impedance pairs from the initial sequence impedance pair exceeding a threshold may also indicate the presence of a fault, regardless of whether a match is confirmed at 710. As above, corrective action may be taken, such as shutting down all or portions of the ESP electrical system, generating a diagnostic report of the type and/or location of the fault, and other similar actions to inform an operator of the identified fault.

[0060] In addition to the foregoing, certain embodiments of the present disclosure may monitor overall pump health through a determination of positive sequence impedance at the motor 26 terminals, which is related to motor slip. In situations where motor slip increases rapidly, it can be assumed that pump health has degraded. However, determination or estimation of motor slip relies in part on processing of current data or accelerometer data in the frequency domain, for example using a fast Fourier transform (FFT), which may be difficult to calculate, unavailable as measurements, or otherwise computationally intensive.

[0061] To address these issues, at least some associated techniques may be based on the approximate equivalent circuit of an induction motor 26 under positive sequence voltage application as shown in the example of FIG. 8. In FIG. 8, the resistance r s represents the stator resistance and is in series with the stator leakage inductance lis, as well the rotor leakage inductance lir and the rotor resistance r r divided by the rotor slip, S. The mutual inductance h is also provided as shown. These values can be computed through known techniques such as through use of an analytical, semi-empirical motor model, which uses as inputs motor winding code information, stator temperature information, and operating condition information {e.g., root mean square voltage and approximate horsepower). The model outputs the various inductances, resistances, and factors.

[0062] The positive sequence impedance at the motor terminals may be expressed as:

Z P * r staor + ja>l ls + (18)

In view of this, the variation of the positive sequence impedance (at the motor terminals) with variation in motor slip may be expressed as:

[0063] It is assumed that the electrical circuit parameters of the model shown in FIG. 8 do not change, and thus a change in the motor slip S results in a variation of similar magnitude to the motor terminal positive sequence impedance Z p . As explained above, the instantaneous motor terminal voltages are estimated from surface voltage measurements. Further, instantaneous positive sequence impedance may also be estimated as described above based on estimated motor terminal voltage and motor terminal current.

[0064] Embodiments of the present disclosure may monitor the positive sequence motor terminal impedance over time to assess a pump health state. For example, as shown in FIG. 9, a threshold may be determined {e.g., experimentally based on a value for positive sequence motor terminal impedance while the pump is in a known, healthy state). As the pump health degrades, motor slip increases, which decreases the magnitude of positive sequence motor terminal impedance. Thus, a positive sequence motor terminal impedance crossing below the threshold causes a warning or alert to be generated indicating that the pump is operating in an unhealthy state. As above, additional corrective action {e.g., shutting off the pump) may be taken upon the positive sequence motor terminal impedance crossing below the threshold.

[0065] Other embodiments may establish a baseline value for positive sequence motor terminal impedance {i.e., when the pump is in a known, healthy state) and generate a warning or alert when the calculated instantaneous positive sequence motor terminal impedance deviates from the baseline value by more than a predetermined threshold. Additional corrective action may also be taken in these embodiments.

[0066] In addition to estimating pump differential pressure based on measured surface and voltage data as explained above, other embodiments may estimate or predict pump health degradation using mechanical and electrical signatures. In particular, vibration signatures are identified from mechanical and/or electrical measurements. In some cases, a change in motor slips may also be identified from real-time electrical measurements.

[0067] FIG. 10 shows an exemplary cross-sectional view of an ESP motor, which includes a rotor winding distribution 812 and a rotor core 813 that rotates inside a stator winding distribution 814 and a stator core 815. An air gap 816 exists between the rotor winding 812 and the stator winding 814. As shown, a condition is demonstrated in which the rotor shaft 817 exhibits orbital motion in addition to the nominal rotation of the rotor 812, 813 itself; this orbital motion is in response to a general degradation in pump health. In particular, a trajectory 810 of the rotor shaft 817 is shown around the stator center, given by the intersection of the X- and Y-axes. The motion caused by the orbital rotation of the rotor shaft 817 around the stator center transfers to the ESP housing by way of the magnetic coupling between the rotor 812 and stator 814 of the motor. Additionally, the orbital rotation of the rotor shaft 817 also influences the current drawn by the motor, due to the magnetic coupling and corresponding induced current between the rotor 812 and stator 814. In the following explanation, certain assumptions may be made relating to a two-pole induction motor-driven ESP pump; however, it will be appreciated that a similar approach may be extended to various types of motors and pumps.

[0068] As shown, r r represents the radius of the rotor core 813 and r s represents the distance from the center of the stator to the stator core 815. The airgap 816 is given by l g , but that value is not uniform due to the orbital motion of the rotor shaft 817. For the purposes of the following explanation, the rotor 812, 813 is assumed to exhibit a simple harmonic motion, where ω ε is the angular frequency of the harmonic motion of the rotor center around the stator center along the x- and y- axes, which results in elliptic eccentricity. Further, ω τ is the angular frequency representing a peripheral motion of the rotor and ω represents the synchronous angular frequency of the stator. This peripheral motion of the rotor is what gives rise to the non-uniform airgap 816, given by l g .

[0069] The following assumes two prominent effects on permeance variation, namely rotor slot impact and dynamic eccentricity due to the orbital motion 810 of the rotor shaft 817. Under these assumptions, permeance may be determined by:

X A rf [l + 6 rt cos(R^ r t

(20)

Where R represents the rotor slot number, dynamic eccentricity e d is elliptical (i.e., varies with stator angle) and thus includes major axis e b and minor axis e a , which correspond to the trajectory

810 shown in FIG. 8, and a nominal permeance is represented by A 0 = -^- .

[0070] Thus, the magnetic field in the motor airgap 816 can be expressed as:

H(0, t) = A Q ] S X [cos(wt 0)]

+ A 0 Js X— [cos((R >r ± <'> t R6

(21) where, J s represents the winding current density predominantly developed by the stator magnetizing current. This derived magnetic field transfers the orbital motion of the rotor shaft 817 to the ESP housing and influences the current drawn by the motor, as will be explained in further detail below.

[0071] A radial force distribution that represents the transfer of the permeance variation to the ESP housing is given by:

where μ 0 represents the permeability of a non-magnetic material (e.g., oil or air). These radial forces are applied to the ESP housing, and thus are detectable (e.g., by an accelerometer) as velocity and acceleration values. Radial force harmonics occur at the frequency ω (corresponding to the harmonic motion around the stator center) and are given by:

σ ωε (0, t) = (2 + e rt 2 )e d cos (oi e t tan "1 tanfl)) (23)

Additional side band frequencies such as ω ε ± 2ω, ω ε ± 4ω, and so on have similar dependencies in magnitude on the dynamic eccentricity e d . Radial force harmonics also occur at the frequency i?a> r (corresponding to the number of rotor slots times the shaft speed of the motor, or the peripheral motion of the rotor) and are given by:

σ ϋ ω τ > ) = ^ (2 + e d 2 )e rt cos(Ra> r t ϋθ) (24) As above, additional side band frequencies such as Λω Γ + 2ω , i?w r + 4ω and so on have similar dependencies in magnitude on dynamic eccentricity e d .

Each of the eccentric frequencies related to ω ε produces a single radial force σ ωε (θ, ί) of frequency ω and its sidebands. By contrast, all of the eccentric frequency effects add up to develop the radial force, a RoJr (e, t) of frequency Rco r and its side bands. The radial force σ ωε (θ, t) and its sidebands may be detected using low- frequency (e.g., for ω = 60Hz, values of ω ε may be, for example, 20-3 OHz) response from an accelerometer depending on mechanical properties of the ESP string, such as stiffness or inertia. For example, a particularly stiff ESP string may produce vibrations of a higher frequency than a less stiff ESP string. On the other hand, the radial force σ Κωτ (β, t) and its sidebands are detected using a higher-frequency accelerometer response (i.e., at the frequency of the shaft speed times the number of rotor slots), again depending on mechanical properties of the ESP string, such as stiffness or inertia. Once the radial force σ Εωγ .(θ, t) has been detected, including its side band frequency responses, embodiments of the present disclosure may utilize such information in determining or estimating pump health.

[0072] Referring now to FIGS. 14 and 15, examples are shown that relate to observations captured during an artificial sand injection test. In particular, the impact on high-frequency vibration components is noted, which are reflected in the below-described indices relating to the velocity values derived from one or more accelerometer readings. In particular, it was observed that high frequency vibration measured at the motor housing was consistently increasing in magnitude with time. Since the pump health degrades fairly consistently until failure, it was determined that the high frequency vibration components are an indication of the pump shaft motion, and thus indirectly an indication of pump health.

[0073] FIG. 14 shows a frequency response plot 1400 for derived velocity and, in particular, more predominant peaks at 1402, 1404, and 1406. The peak 1402 corresponds to the response at 1258Hz (i.e., the number of rotor slots (22) times the shaft speed of approximately 57.2Hz in this case) and the peaks 1404, 1046 correspond to sidebands at +/- two times the line frequency, or 60Hz in this example. Another peak 1408 exists at 1018Hz, or four times the line frequency from the peak 1402. These spectral components generally increase in magnitude as pump degradation (manifested as shaft eccentricity in this case) increases. In certain cases, and as suggested by experimental data, the strongest peak may not necessarily be at R > r as is the case in FIG. 14, but rather at one of the sideband frequencies. In one exemplary dataset, the line frequency was 60Hz while the running speed was 58.375Hz, resulting in Ro> r of 1285Hz based on 22 rotor slots with sidebands of 1 165Hz and 1405Hz. It was noted that the sideband of 1405Hz was the dominant spectral component. The frequency at which the response is highest generally depends on the stator modes and natural frequencies. For example, if one of the sidebands is close to a natural frequency, then the response at that sideband frequency may be greater than the Rco r component.

[0074] As explained, each of the radial forces described above may be captured by an accelerometer, resulting in a particular accelerometer response or acceleration signature. Integration of such an acceleration signature results in a velocity V at each frequency of the response. In accordance with embodiments of the present disclosure, a health indicator /is formed based on the frequency responses of an accelerometer proximate to the ESP motor. Different indicators / may exist to capture the frequency response at particular frequencies of interest as explained above, including Rw r , its sideband frequencies, and other frequencies proximate to ?ω Γ . In certain embodiments, an overall indicator /may be a combination of several different indicators based on the velocity Fat a particular frequency:

h = V R(0r (e, t) (25)

(0, t) 2 (26)

[0075] Referring to Equation 25, the indicator h represents the vibration velocity component at a frequency equal to the number of rotor slots {e.g., 22) times the running speed of the pump. The velocity component may be given in various units, for example meters/second or inches/second. In some embodiments, the indicator is monitored during a known, healthy pump condition (e.g. , initially after installation) to develop a known baseline or healthy value of the indicator I\. Then, subsequent deviations from the baseline value (e.g., beyond a predetermined threshold of change or exceeding a predetermined threshold absolute value) may cause a warning to be generated or other corrective action taken. Further, while the indicator is velocity-based in nature, certain embodiments may instead utilize the direct acceleration value at the same frequency.

[0076] Referring to Equation 26, the indicator h further leverages the discovery that in addition to the velocity (or acceleration) component at the frequency equal to the number of rotor slots {e.g. , 22) times the running speed of the pump, the sideband components at twice and four times the electrical line frequency {e.g., 60Hz) away may also contain significant vibration components that increase with degradation over time. In fact, in certain examples, the sideband vibration components may be more pronounced than even the component at Rco r . As above, V refers to velocity (for example in m/s or in/s) at the frequency component indicated by the subscript. In this particular indicator, five discrete frequencies are analyzed, although the scope of the present disclosure need not be limited to only those discrete frequency components and, in fact, other frequency components may be additionally be considered. Further, and as above, the indicator h may be normalized to a baseline value determined during a known, healthy pump condition. Then, subsequent deviations from the baseline value {e.g., beyond a predetermined threshold of change or exceeding a predetermined threshold absolute value) may cause a warning to be generated or other corrective action taken.

[0077] Referring to Equation 27, the indicator addresses a practical limitation where it may be difficult or impossible to accurately determine the actual operating speed of the pump. In particular, the sum of velocity (or acceleration) components over a range of frequencies is considered. The range of frequencies may be selected to include Ro) r and its sideband components. However, since the particular value of the pump operating speed may not be accurately determinable, Equation 27 suitably captures all velocity components at frequencies near an approximate value of Λω Γ . The actual range of component summation may be greater or less than that explicitly shown in Equation 27, and it should be appreciated that the scope of the present disclosure is not limited to any particular range of values. Further, and as above, the indicator h may be normalized to a baseline value determined during a known, healthy pump condition. Then, subsequent deviations from the baseline value (e.g., beyond a predetermined threshold of change or exceeding a predetermined threshold absolute value) may cause a warning to be generated or other corrective action taken.

[0078] FIG. 15 demonstrates an exemplary trending of I\ and h over time, both using measured acceleration responses as well as derived velocity responses (e.g., by integrating the acceleration response). The plot 1500 shows the original measured or derived values, while the plot 1510 shows the values of the plot 1500 in a normalized manner. For purposes of simplicity, is not shown; however, h demonstrates similar trends to I\ and , and may be particularly useful where the actual operating speed of the pump is unknown. It is noted that the indices generally increase over time, which may be consistent with pump health degradation.

[0079] For example, when the ESP begins to operate, lis generally a flatline over time when the pump is known to be healthy. Monitoring of the indicator / begins at this time and, as the health of the pump degrades over time (e.g. , due to bearing wear or other mechanical problems), the value of / tends to increase over time. In particular, the speed of the shaft ω Γ is sensed, for example by the MCSA or maximum low-frequency accelerometer spectral data. As explained with regard to FIG. 10, as the pump degrades, the eccentricity e d increases, resulting in an increase in the fault indicator, I. The accelerometer can be placed on the motor, pump, protective cover, and the like. Data from the accelerometer may be transferred back to the surface using the gauge described above. When the value of / increases beyond a certain threshold value (or exceeds a threshold value of change from an initial baseline), a warning may be generated and presented to a user to perform further diagnostics on the ESP system. For example, / may behave over time similarly to the fault indicator F.I. shown in FIG. 6. In some cases, corrective action may be taken when the value of / exceeds a threshold, such as shutting off the motor and pump.

[0080] In addition to detecting and analyzing vibration characteristics using an accelerometer as described above, other embodiments of the present disclosure leverage the fact that variations in permeance are also transferred to motor-induced electromagnetic fields (EMFs). The induced EMF e v for each motor phase (assuming a full pitched coil in which two sides of a coil are 180 degrees apart, electrically) due to vibrations at the frequency ω ε is given by: e,(t) = - Γ ^ ^ (ω ± ω ε ε α e b ) x [sim ± ω ε )ϋ)] (28)

[0081] The induced flux for the motor is defined as:

_ |e v (t)| _ τ 5 μ 0 Λ 0 ] 3 π , Λ , .

v - (^) " €a €b) (2y)

In particular, then, the induced flux for the motor is a function of the eccentricity of the shaft motion, due to its reliance on e a e b .

[0082] Each vibration frequency ω ε introduces two side bands of induced EMFs at frequencies ω ± ω £ . In view of this, a value for induced flux attributed to symmetrical vibration, or where e a =e b , may be given by: ^^ (6 a ) and ν \ ω=ω+ωε = 0 (30)

[0083] Similarly, a relation between induced flux values attributed solely to full asymmetric vibration, or where one of e a or e b is equal to 0, may be given by:

ν\ω=ω-ω 6 ν\ω=ω+ω ε (31)

[0084] As a result, for all vibration both symmetric and asymmetric, or where e a and e fc are nonzero, the induced flux follows the inequality:

ν\ω=ω-ω ε ν\ω=ω+ω (32)

[0085] Since the induced flux for the motor is a function of the eccentricity of the shaft motion, which increases with degradation, embodiments of the present disclosure may generate a health indicator based on the induced flux at particular identified vibration frequencies related to the stator synchronous frequency ff. To identify vibration frequencies of interest, motor terminal voltage is estimated from surface voltage as explained above. A fast Fourier transform (FFT) of motor terminal phase voltage and current is performed. As a result, at any frequency / (in Hz), the motor terminal voltage vector resulting from a complex FFT is given by:

V(f) = V Re + jV Im (33)

[0086] Similarly, the motor current vector at any frequency /is given by:

[0087] The resulting motor back EMF vector at any frequency /is given by:

E f) = V(n+I(f) x Ztf (35) [0088] The impedance at each frequency may be estimated in many ways, for example impedance may be estimated using skin effect compensation based on DC resistance and self- inductance of the motor per phase stator as follows:

Z(f = R dc x - 1 ^ + j2nfL (36)

[0089] The resultant induced flux at any frequency /, may thus be calculated as: O -™ 07)

[0090] FIG. 11 shows an example result 1100 of an estimation of the induced flux as a function of frequency. The estimation 1 100 of induced flux demonstrates local peaks of induced flux value 1102a, 1 102b, which correspond to the side bands of the vibration frequency. Embodiments of the present disclosure generate a health indicator IE based on the induced flux values at the identified side band vibration frequencies as follows:

Similar to other health indicators described above, when the ESP begins to operate, IE may be a level or flat over time when the pump is known to be healthy. Monitoring the indicator IE begins at this time and, as the health of the pump degrades over time (e.g., due to bearing wear or other mechanical problems), the value of IE tends to increase over time as the induced flux at those particular identified frequencies also increases. When the value of IE increases beyond a certain threshold value, a warning may be generated and presented to a user to perform further diagnostics on the ESP system. For example, IE may behave over time similarly to the fault indicator F.I. shown in FIG. 6. In some cases, corrective action may be taken when the value of IE exceeds a threshold, such as shutting off the motor and pump. [0091] Various methods and approaches have been described that detect early signs of wear or failure in an ESP system. These approaches leverage measured mechanical values, measured electrical values, and estimations of electrical values in order to improve ESP health monitoring and prediction. Although several embodiments have been described, it should be appreciated that the scope of the present disclosure also includes various combinations of such embodiments. FIG. 12 shows an exemplary system 1200 including a pump health assessment algorithm 1202 that receives as input health indicators calculated using the above-described techniques, in addition to certain measured quantities. For example, the pump health assessment algorithm 1202 receives the health indicator / generated based on accelerometer data 1204 as explained above. The pump health assessment algorithm 1202 also receives the health indicator h generated based information relating to vibrations derived from surface electrical measurements 1206. The pump health assessment algorithm 1202 also receives the impedance pair 1208 for comparison against a database of impedance pairs known to correspond to electrical faults. The pump health assessment algorithm 1202 further receives the estimation of expected healthy pump differential pressure 1210 derived from surface electrical measurements for comparison with an actual pump differential pressure 1212.

[0092] Based on these inputs, the pump health assessment algorithm 1202 generates an overall indication of pump health, which may be a value of a health spectrum {i.e., a range of values indicating relative health of the ESP system), a binary value indicating whether failure is imminent, or other type of assessment of overall ESP system health. The pump health assessment algorithm 1202 may be a learning-type or artificial intelligence-based algorithm. Various ones of the calculated or derived indicators may be assigned various weights of importance, depending on their particular contribution to an overall determination of whether the ESP is in a healthy mode of operation. Certain embodiments may isolate electrical failures from mechanical faults, based on which indicator is affected by a particular change in ESP operation. The scope of the pump health assessment algorithm 1202 is not intended to be limited to any particular combination of indicators or factors.

[0093] FIG. 13 provides a system schematic of the motor monitor processing system 100 in accordance with an embodiment. The system 100 includes a processing resource 1302 coupled to a non-transitory storage device 1304. The processing resource 1302 may be a single processor, a multicore processor, a single computer (desktop computer, notebook computer, tablet computer, etc.) multiple computing devices coupled together in a network, or any other type of computing device. The non-transitory storage device 1304 includes volatile storage such as random access memory (RAM), non- volatile storage such as a magnetic storage (e.g., hard disk drive), an optical storage device (e.g., compact disc), or solid state storage (e.g., flash storage). The non-transitory storage device 1304 may be a single device or collection of multiple devices, and be either standalone storage devices or storage devices contained within the processing resource 1302.

[0094] The non-transitory storage device 1304 contains motor assessment software 1306 that, when executed by the processing resource 1302, causes the processing resource to perform some or all of the functionality described herein. As one example, the processing resource 1302 can estimate pump differential pressure based on various inputs such as surface measured voltages and currents, and other values as described herein. Of course, the processing resource 1302 may also perform any functionality described herein and is not limited to any particular approach or combination of approaches. Alerts also can be generated or caused to be generated by the processing resource 1302, and the operation of the motor may be adjusted accordingly, as described above. [0095] In embodiments, a non-transitory storage device contains software that, when executed by a processing resource, causes the processing resource to estimate the voltage of a downhole motor for each of multiple phases based on measurements of voltage and current from a multiphase power drive configured to power the downhole motor, extract positive and negative sequence voltage and current from the estimated voltage of the downhole motor and from the measured current value, estimate a differential pressure across a downhole pump powered by the downhole motor based on the extracted positive and negative sequence voltage and current, and generate a signal to adjust operation of the downhole motor based on the estimated differential pressure across the pump.

[0096] The software, when executed by the processing resource to estimate the differential pressure, may further cause the processing resource to compute a torque value based on the extracted positive and negative sequence voltage and current and determine an estimate of the differential pressure based on the computed torque, a specific gravity of pumped fluid, and an estimate of motor speed. The software, when executed by the processing resource, may further cause the processing resource to compute an output power of the motor based on the computed torque value and the estimate of motor speed. The software, when executed by the processing resource to compute the torque value, may still further cause the processing resource to compute a direct current (DC) torque based on the extracted positive sequence voltage and current, compute a DC torque based on the extracted negative sequence voltage and current, and sum the computed DC torques based on the extracted positive and negative sequence voltage and currents to produce a total electromagnetic DC torque. The software, when executed by the processing resource, may further cause the processing resource to subtract a viscosity drag force from the total electromagnetic DC torque to compute the torque value. In some cases, the software, when executed by the processing resource, causes the processing resource to estimate an expected healthy differential pressure across the pump based on the estimated voltage of the downhole motor, the measured current value, and an average specific gravity of pump fluid during a time interval proximate to the estimation of the healthy pump pressure head. Still further, the software, when executed by the processing resource, further causes the processing resource to compute a fault indicator based on the difference between an actual differential pressure across the pump and the estimated expected healthy differential pressure across the pump and adjust operation of the downhole motor based on the fault indicator.

[0097] In other embodiments, a non-transitory storage device contains software that, when executed by a processing resource, causes the processing resource to estimate the voltage of a downhole motor for each of multiple phases based on measurements of voltage and current from a multi-phase power drive configured to power the downhole motor; extract positive, negative, and zero sequence voltage and current from the estimated voltage of the downhole motor and from the measured current value; determine positive, negative, and zero sequence impedances based on the positive, negative, and zero sequence voltages and currents, respectively, to thereby produce a complex sequence impedance pair; and generate a signal to adjust operation of the downhole motor based on the complex sequence impedance pair.

[0098] The software, when executed by the processing resource, may cause the processing resource to identify an electrical fault type or location based on the complex sequence impedance pair. The software, when executed by the processing resource, may further cause the processing resource to compare the complex sequence impedance pair to a database of experimentally- determined impedance pairs indicating one or more electrical fault types or one or more electrical fault locations. Still further, the software, when executed by the processing resource, causes the processing resource to determine a baseline sequence impedance pair when a pump driven by the motor is in a known, healthy state and generate a signal to adjust operation of the downhole motor when a subsequent sequence impedance pair deviates from the baseline sequence impedance pair by more than a predetermined amount.

[0099] In certain embodiments, a non-transitory storage device contains software that, when executed by a processing resource, causes the processing resource to estimate the voltage of a downhole motor for each of multiple phases based on measurements of voltage and current from a multi-phase power drive configured to power the downhole motor, extract positive sequence voltage and current from the estimated voltage of the downhole motor and from the measured current value, determine positive sequence impedance at terminals of the motor based on the positive sequence voltage and current, and generate a signal to adjust operation of the downhole motor based on the positive sequence motor terminal impedance.

[00100] The software, when executed by the processing resource, may further cause the processing resource to determine a baseline positive sequence motor terminal impedance value when a pump driven by the motor is in a known, healthy state and generate a signal to adjust operation of the downhole motor when a subsequent positive sequence motor terminal impedance value deviates from the baseline positive sequence motor terminal impedance value by more than a predetermined amount. The software, when executed by the processing resource, may also cause the processing resource to generate a signal to adjust operation of the downhole motor when the positive sequence motor terminal impedance value decreases below a predetermined threshold value.

[00101] Other embodiments include a non-transitory storage device containing software that, when executed by a processing resource, causes the processing resource to calculate a velocity component at a frequency based on acceleration data received from an accelerometer coupled to a component of an electric submersible pump comprising a motor having a rotor and a stator, the acceleration data indicative of a harmonic motion of the rotor around the stator, wherein the frequency is greater than a pump operating frequency. The software also causes the processing resource to determine a health indicator based on the calculated velocity component and generate a signal to adjust operation of the motor based on the determined health indicator.

[00102] The frequency may be equal to a number of rotor slots of the motor times a running speed of a pump driven by the motor. The software, when executed by the processing resource, may further cause the processing resource to calculate a plurality of velocity components at a frequency given by a number of rotor slots of the motor times a running speed of a pump driven by the motor and sideband frequencies that differ from that frequency by a multiple of an electrical line frequency for the motor and determine a health indicator based on the plurality of velocity components. The software, when executed by the processing resource, may also cause the processing resource to calculate a plurality of velocity components for a range of frequencies surrounding a frequency given by a number of rotor slots of the motor times a running speed of a pump driven by the motor and determine a health indicator based on the plurality of velocity components calculated over the range of frequencies. The software, when executed by the processing resource, may further cause the processing resource to determine a baseline health indicator based on the calculated velocity component when a pump driven by the motor is in a known, healthy state and generate a signal to adjust operation of the motor when a subsequent health indicator value deviates from the baseline health indicator value by more than a predetermined amount. The software, when executed by the processing resource, may still further cause the processing resource to generate a signal to adjust operation of the motor when the health indicator value increases above a predetermined threshold value.

[00103] Still other embodiments include a non-transitory storage device containing software that, when executed by a processing resource, causes the processing resource to estimate the voltage of a downhole motor for each of multiple phases based on measurements of voltage and current from a multi-phase power drive configured to power the downhole motor; determine a motor terminal voltage vector and a motor terminal current vector based on the estimated voltage of the downhole motor and from the measured current value; determine an induced flux of the motor based on the voltage vector and current vector, the induced flux having a plurality of frequency components; estimate frequencies of the plurality of frequency components for which the induced flux comprises a localized peak value; determine a health indicator based on the induced flux values at the estimated frequencies; and generate a signal to adjust operation of the downhole motor based on the determined health indicator.

[00104] The frequency may be equal to a number of rotor slots of the motor times a running speed of a pump driven by the motor. The software, when executed by the processing resource, may further cause the processing resource to determine a baseline health indicator based on the induced flux values at the estimated frequencies when a pump driven by the motor is in a known, healthy state, and generate a signal to adjust operation of the motor when a subsequent health indicator value deviates from the baseline health indicator value by more than a predetermined amount. The software, when executed by the processing resource, may cause the processing resource to generate a signal to adjust operation of the motor when the health indicator value increases above a predetermined threshold value. [00105] Other embodiments include a motor monitor processing system comprising a storage device storing executable code and a processing resource coupled to the storage device. The processing device is configured to estimate the voltage of a downhole motor for each of multiple phases based on measurements of voltage and current from a multi-phase power drive configured to power the downhole motor, extract positive and negative sequence voltage and current from the estimated voltage of the downhole motor and from the measured current value, estimate a differential pressure across a downhole pump powered by the downhole motor based on the extracted positive and negative sequence voltage and current, and generate a signal to adjust operation of the downhole motor based on the estimated differential pressure across the pump.

[00106] In other cases, the processing resource is configured to estimate the voltage of a downhole motor for each of multiple phases based on measurements of voltage and current from a multi-phase power drive configured to power the downhole motor; extract positive, negative, and zero sequence voltage and current from the estimated voltage of the downhole motor and from the measured current value; determine positive, negative, and zero sequence impedances based on the positive, negative, and zero sequence voltages and currents, respectively, to thereby produce a complex sequence impedance pair; and generate a signal to adjust operation of the downhole motor based on the complex sequence impedance pair.

[00107] The processing resource may also be configured to estimate the voltage of a downhole motor for each of multiple phases based on measurements of voltage and current from a multiphase power drive configured to power the downhole motor, extract positive sequence voltage and current from the estimated voltage of the downhole motor and from the measured current value, determine positive sequence impedance at terminals of the motor based on the positive sequence voltage and current, and generate a signal to adjust operation of the downhole motor based on the positive sequence motor terminal impedance.

[00108] In some cases, the processing resource is configured to estimate the voltage of a downhole motor for each of multiple phases based on measurements of voltage and current from a multi-phase power drive configured to power the downhole motor, determine a motor terminal voltage vector and a motor terminal current vector based on the estimated voltage of the downhole motor and from the measured current value, determine an induced flux of the motor based on the voltage vector and current vector, the induced flux having a plurality of frequency components, estimate frequencies of the plurality of frequency components for which the induced flux comprises a localized peak value, determine a health indicator based on the induced flux values at the estimated frequencies, and generate a signal to adjust operation of the downhole motor based on the determined health indicator.

[00109] The motor monitor processing system may also include an accelerometer configured to generate acceleration data and coupled to a component of an electric submersible pump comprising a motor having a rotor and a stator. The processing resource may thus be configured to calculate a velocity component at a frequency based on the acceleration data, the acceleration data indicative of a harmonic motion of the rotor around the stator, wherein the frequency is greater than a pump operating frequency; determine a health indicator based on the calculated velocity component; and generate a signal to adjust operation of the motor based on the determined health indicator.

[00110] Certain ones of the techniques described herein permit the computation of the variables at each sampling instant without storing a long length value of current and voltage as well as statistical data, and for those techniques use of statistical data is negligible. As such, the computation flowrate and other parameters described herein can be computed quickly and efficiently. Other ones of the techniques may additionally or alternatively utilize pump curve data, which may reflect statistical data for a particular pump in particular and varying operating conditions.

[00111] Although only a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from the electrical connector assembly. Features shown in individual embodiments referred to above may be used together in combinations other than those which have been shown and described specifically. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims.

[00112] The embodiments described herein are examples only and are not limiting. Many variations and modifications of the systems, apparatus, and processes described herein are possible and are within the scope of the disclosure. Accordingly, the scope of protection is not limited to the embodiments described herein, but is only limited by the claims that follow, the scope of which shall include all equivalents of the subject matter of the claims.