T cover the specification of electrical submersible pump

Transcription

1 282 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 28, NO. 2, MARCHIAPRIL 1992 Correlations of Submersible Cable Performance to Neer-McGrat Ampacity Calculations Gordon C. Baker and Marcus. Duram, Senior Member, ZEEE Abstract-Te configuration and application of electric submersible pump cable demands careful consideration of temperature effects on te cable materials. Tests ere conducted to develop correlation factors and modifications to te Neer-Mc- Grat termal model. Tese disclose te unique features of te cable. A series of equations are presented. Application carts are provided to assist te user in proper selection of te cable. NOMENCLATURE 17. cross sectional area of copper in a conductor (circular mil) (see Table I) diameter of conductor (inces) (see Table I) diameter over te armor (inces) NOTE: round and flat cables use different equations to calculate te Oar diameter over te jacket NOTE: round and flat cables use different equations to calculate te Djk termal resistivity of insulation, constraining coverings, and jacket 5 C cm/att cable lay factor, for round cables = 1.2 conductor resistance at conductor temperature (oms per foot) tickness of armor (inces) insulation tickness (inces).9 for 5 volt insulation rating jacket tickness (inces).6 for submersible cable restraining covering tickness (inces).1 for tese calculations temperature of ambient surroundings ( " C) temperature of te conductor ("C) te mean temperature across te gas area ("C) temperature coefficient of zero resistance for copper circular mil oms per termal resistance of te gas zone beteen te cable surface and te surrounding casing pipe Paper PID 91-15, approved by te Petroleum and Cemical Industry Committee for presentation at te 199 Petroleum and Cemical Industry Tecnical Conference, Houston, TX, September Manuscript released for publication Marc 13, G. C. Baker is it Pillips Cables Ltd., Brockville, Canada K6V 54. M.. Duram is it Teay Corporation, and te University of Tulsa, Tulsa, OK IEEE Log Number TABLE I CONDUCTOR MEASUREMENTS Circular AG Configuration mil Area Diameter #6 solid " #4 solid " #2 stranded " #1 stranded " # 1 IO stranded " TR TR, termal resistance of te insulation termal resistance of te jacket. INTRODUCTION HERE ARE THREE IEEE Recommended Practices tat T cover te specification of electrical submersible pump cables. Te Recommended Practices address polypropylene insulated cable, etylene-propylene insulated cable, and field testing of te cable. Tese Recommended Practices ave recently undergone a five-year revie. In an attempt to provide more accurate data, a number of tests ere conducted. Te results of tese tests ere used to develop correlation factors for use in te Neer-McGrat relationsip. AMPACITY CALCULATIONS Te useful orking life of any cable is adversely affected by te operating temperature of te cable. Excessive conductor temperature may irreversibly damage te cable insulation and jacket. Submersible pump cables are applied in ars environments it ig ambient temperatures. Te ambient in conjunction it conductor eat rise makes effective application of submersible cable a tedious process. Tis paper provides te cable user it a metod to estimate te maximum conductor temperature for te submersible pump cable application. Te ampacity calculations are developed from te Neer- McGrat formula (see eq. 9 of [l]). Teir equations ere based on ork derived in te early 193's for ig-voltage poer cables. Neverteless, teir paper as first presented in 1957 at an IEEE (NEE) meeting in Montreal, Canada. Teir equation for cable ampacity is identified: Z conductor current (amperes) /92$ IEEE

2 BAKER AND DURHAM: CORRELATIONS OF SUBMERSIBLE CABLE PERFORMANCE 283 Ta TC Td RdC 1 + Y, TR temperature of ambient surrounding cable ("C) temperature of conductor ("C) temperature rise of conductor due to dielectric loss ("C) dc resistance of conductor at conductor operating temperature T, (oms per foot) ac/dc resistance ratio termal resistance (per conductor) beteen te conductor and ambient (termal-om-foot). te cable. To compensate, te conductor resistance is increased by 2 %. Tis inflation is incorporated into a cable lay factor (LF). Te accepted factor for submersible cable is 1.2. Te tisting and lengt increase does not apply to flat cables. Terefore, te lay factor is one. Te modified conductor resistance may be expressed as follos (see eq. 1 and Table I in [l]). Te resistance is measured in oms per foot at te conductor temperature: MODIFIED CALCULATIONS Te Neer-McGrat relationsips are modified for submersible cable. Some of te calculations ill be more complex. Hoever, several assumptions can be made to simplify te ampacity calculations for pump cable applications. Te 6-to-5-V range used in pump cables allos te removal of te dielectric loss portion of te original equation. Te actual dielectric losses are very small. Terefore, te temperature rise due to dielectric Td may be neglected. Submersible cable conductors range in size from #6 to # 1/ AG. For tis configuration, te ac/dc ratio is almost equal to one [4]. Tus, te (1 + Y,) term becomes unity. For submersible pump cables, te ampacity equation ten simplifies as follos: I = sqrt[ (T,- To)/( Rd, * TR)]. (2) Tere are a number of terms and abbreviated symbols used in developing te relationsip. Te Appendix contains an alpabetic listing of tese symbols. Numeric values are given constant terms are employed. Eac of te terms ill be analyzed in detail. Te most complex component of te equation is te termal resistance (TR). Tis parameter incorporates te pysical caracteristics of te cable as ell as te application configuration. TEMPERATURE OF CONDUCTOR Since te surface of te metal conductor ill be te ottest spot itin te cable, te surface temperature of te conductor must be restricted to protect te insulation and jacket. Te maximum rated conductor operating temperature T, is dependent on te submersible pump cable construction. Polypropylene (PP) insulated cables ave a rated maximum operating conductor temperature of 96 C (25 OF) [61. Etylene Propylene Diene Monomer (EPDM) is commonly referred to as EPR insulated cable. Tese designs may operate at muc iger temperatures. An accepted maximum rated conductor operating temperature for EPDM insulated and nitrile jacketed cable is 14 C (284 F) [7]. CONDUCTOR RESISTANCE During te ampacity determinations, conductor resistance is calculated at te maximum conductor temperature. Te conductor resistance relationsips are based on uncoated copper. It is assumed tat te increase in actual resistance due to coating of te conductors is negligible. For round cables, derivation of te conductor resistance must include corrections for lengt of ire. Te tisting of te cable conductors effectively increases te actual lengt in - (LF) * * ( T,) A, * (4) LF cable lay factor R,, resistivity of copper at 2 C Tzr temp coefficient of zero resistance for copper T, conductor temperature ("C) A, cross sectional area of te conductor (circular mils). AMBIENTEMPERATURES Te ambient temperature surrounds te cable. Te value of te ambient is often assumed to be te static bottom ole temperature. Hoever, in a donole environment, te ambient temperature depends not only on te bottom ole conditions but on a number of oter factors. Te temperature gradient from te perforations to te cable, te eat rise from te submersible equipment, and te eat generated from te cable all ave an effect on te ambient temperature. For te ampacity calculations carried out in tis project, T, may vary from 4 C (14 F) to 14 C (284 F). THERMAL RESISTANCE For submersible applications, te TR value consists of tree parts. Tese components are te insulation TR,, jacket TR,, and te gas zone beteen te cable and pipe casting TR, PI. TR is expressed in termal-om-feet (tof): TR = TR, + TR, + TU, (5) TR, TR of te insulation TR, TR of te jacket TR, TR of gas zone beteen te cable surface and surrounding casing pipe. THERMAL RESISTANCE OF THE GAS ZONE Cable tat is installed itin a metal conduit, suc as a ell casing, as some contact it te metal surface. Hoever, muc of te cable is exposed to te gas itin te conduit. Te eat transfer caracteristics of te gas zone dramatically affects te ability of te cable to dispose of eat. From te original Neer-McGrat paper, an expression for calculating TR, may be obtained (see eq. 41 of [l]). Te

3 284 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 28, NO. 2, MARCH/APRIL 1992 units are tof TRg=3*A/[1+ {(B+ (C*Tm))*Da,}] (6) A, B, and C are constants. Te article (see Table VI1 of [l]) provides numeric values for te A, B,C terms under some conditions. For example, a cable in an air-filled metal conduit as constants A = 17., B = 3.6, and C =.29. Tis configuration is most similar to a submersible cable operating above te fluid level of te ell. Mean Temperature Te parameter T, symbolizes te mean temperature across te gas area. Te result is dependent on te temperature of te cable conductor T, and te ambient temperature T,. Many of te values used must be experimentally developed since eac application is different. Tests ere conducted by placing a termocouple in te air space. Te termocouple as 1 in from te cable. An experimental factor of.3 as necessary to correct te mean temperature parameter. Te mean temperature (T,) is no defined: T, = T, + [(T, - T,) *O.3]. (7) Diameter Te parameter D,, depicts te diameter (in inces) over te armor. For PP and EPDM insulated cables, te insulation tickness t, is set at.9 in. Tis measurement is caracteristic of 5OOO-V rated cables. Calculations made it.75-in cable, ic is te insulation tickness of 3OOO-V rated cables, do not appreciably alter te end result. Typically, submersible pump cable constructions include a constraining covering it a tickness t, over te insulation. It is assumed tat tis layer adds anoter.1 in to te insulation all. For PP and EPDM insulated round and flat cables, te jacket tickness ti is set at.6 in. Te nominal armor strip tickness t,,, is.25 in for round cables. To compensate for te armor interlocking profile, an additional.6 in is included in te summation. ~ Considering all tese components, te diameter over round cable armor D,, may be calculated as follos. Te dimensions are in inces: Oar = [d + (2*t,) + (2" t,)] * (2* t,) + (4* tu,,) +.6" (8) side primarily exposed to te gas zone: Oar= [d+ (2*t;) + (2*t,)] + [2*Tj] + [4*t,,,]. THERMAL RESISTANCE OF THE INSULATION FOR ROUND CABLES (9) An expression for calculating te termal resistivity of te insulation TR, of round cables may be obtained from te Neer-McGrat paper (see eq. 39 of [l]). Te reference assumed copper ad a constant temperature coefficient. Te relationsip is modified for variations in te termal resistivity: TR, =.14 * t, insulation tickness t, restraining coverings tickness t, jacket tickness over te insulation tu,, tickness of armor d diameter of conductor. A different procedure is used to determine te diameter over flat cable armor. Furtermore, tere is a difference in te armor tickness. Te nominal armor strip tickness t,,, diminises to.2 in. Te D,, measurement is taken in te flat direction. Tis orientation is used since te cable is mounted it te flat TR, =.52 * * G, * TCF (1) q termal resistivity of insulation material 5 "C cm/ (see Table VI of [l] and see [3]) G, geometric factor TCF temperature correction factor. A matematical formula for calculating te geometric factor is as follos (see [5] and eq. 8 of [l]): G, = 2.31g,, [3 * (G, + l)] (11) [(8*(ti+t,)) +t,]*[t,+t,+t,] G, = 4*d*(ti+ t,). (12) A correction factor (TCF) as been developed to compensate for canges in te termal resistivity it temperature. Te factor is a matematically derived number based on te positioning of te tree conductors and te ratios of tickness of te insulation to te diameter of te conductors: TCF= (d*1 + T,)/T, (13) d is te diameter of te conductor (in inces), and T, is te temperature of te conductor ("cl. THERMAL RESISTANCE OF THE JACKET FOR ROUND CABLES From te original reference, an expression for calculating te termal resistance of te jacket TR, for round cables may be obtained (see eq. 4 of [l]). Again, te TCF as been included to compensate for canges in te termal resistivity it temperature: * 3 * [ t, / ( Djk - ti) ] * TCF ( 14) t, is te jacket tickness over te insulation, and Djk is te diameter of te jacket. Te diameter over te jacket Dik for round cables may be represented by Djk= [d+ (2*t,) + (2*t,)] * [2*tj]. (15) THERMAL RESISTANCE OF THE JACKET AND INSULATION FOR FLAT CABLE Te TR, and TR, values are different for flat and round cables. Neer and McGrat presented an expression for

4 BAKER AND DURHAM: CORRELATIONS OF SUBMERSIBLE CABLE PERFORMANCE 285 I6 v) E 14 a E 12.U c- 1 2 P: e: b% U I5 I Fig. 1. calculating TRi and TR, of flat cables. It is assumed tat te termal resistivity of te insulation, jacket, and any reinforcing layers are equal. For flat cables, te termal resistance of te insulation and jacket (TR, and TR,) are lumped togeter into one equation. Te referenced expression as derived for flat cable configurations used in ig-voltage systems. Tese types of cables are not closely spaced like te tree conductors in a flat pump cable. Te termal resistance ould be different in MAXIMUM ELL TEMPERATURE (F) Ampacity for round cable, polypropylene, 25F conductor. te center insulated conductor. 5 4 For pump cable calculations, it as traditionally been g 2 assumed tat termal resistance for eac conductor is equal. U Hoever, experimentation as proven tat te center conductor does get sligtly armer tan te outer to conductors. Te resistance (per conductor) Of te and Fig. 2, Ampacity for flat cable polypropylene, 25F conductor, te jacket for flat cables may be calculated as follos (see eq. 38 of [l]): TR, + TR, =.12 * q *log (Djk/d)* TCF. (16) Te value of Djk is calculated based on te insulation tickness, te overlying, constraining coverings or braids, and te jacket tickness. For flat cables, te diameter over te jacket Djk may be establised: Djk = [ d + (2 * ti) + (2 * tr)] + [2 * t,]. (17) AMPACITY CHARTS Using te derived ampacity equations, a series of ampacity curves may be generated. Four suc graps are displayed. Figs. 1 and 2 are ampacity carts for round and for flat polypropylene insulated-pump cables, respectively. Te plots exibit te maximum current loading for different conductor sizes. Tese graps ere derived using a conductor temperature of 25 F. Te ampacity curves for round and for flat EPDM-insulated, nitrile rubber-jacketed pump cables are given in Figs. 3 and 4. Te carts depict te maximum current loading for different conductor sizes. Tese plots ere derived using a conductor temperature of 284 F. EXPERIMENTAL A series of experiments ere conducted to verify te applicability of te correlation factors tat ere applied to te v z; loo g P: 14 a 3 12 b 1 z 6 g BO e: g MAXIMUM ELL TEMPERATURE (F) v o I5 17 I MAXIMUM ELL TEMPERATURE (F) Fig. 3. Ampacity for round cable, EPDM, 284F conductor. original termal model developed by Neer and McGrat. Tese test ere conducted it termocouples applied to conductors and placed in ambient gas. Tese tests provided te basis for te correction factor. CONCLUSIONS Te procedures tat ave been introduced ill provide te user it te metod to estimate te conductor temperature of a submersible pump cable. Cable life can be extended by

5 286 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 28, NO. 2, MARCHIAPRIL 1992 I6 UY U 14 a 5 12 v c- LOO z g 8 6 U g 2 U n MAXIMUM ELL TEMPERATURE (F) Fig. 4. Ampacity for flat, EPDM, 284F conductor. not subjecting te materials to termal abuse. A series of calculations and conversion factors are presented. Tese modify te Neer-McGrat equations for te unique configuration of electric submersible pump cable. From te correlations, a series of ampacity carts are arrayed. Te curves and equations are a tool for te production or field engineer to assist in te proper selection and operation of an electrical submersible pump system. REFERENCES J. H. Neer and M. H. McGrat, Te calculation of te temperature rise and load capacity of cable systems, J. Poer App. Syst., Oct R. Beer and R. Trapp, Proposed formula for oil ell cable, Mar. 1985, personal communication. D. McAllister, Electrical Cables Handbook. London: Granada, 1982, Table 8.2. D. G. Fink and H.. Beaty, Standard Handbook for Electrical Engineers (12t ed.). Ne York: McGra Hill, Table D. S. Simons, Cable geometry and te calculation of current carrying capacity, AIEE Trans., June IEEE Recommended Practice for Specifying Electric Submersible Pump Cable-Polypropylene Insulation, IEEE STD 119. Ne York: IEEE. IEEE Recommended Practice for Specifying Electric Submersible Pump Cable-Etylene Polypropylene Rubber Insulation, IEEE STD 118. Ne York, IEEE. Gordon C. Baker received an Honors Bacelor of Science degree in cemistry from Queens University, Kingston, Canada. He is an Applications Engineer for Pillips Cables Limited, Brockville, Canada. He as previously publised four papers on mining and submersible cable applications. Mr. Baker is a Carter Cemist (CCem) in Canada. He is a past member of ASTM and te American Cemical Society. He as been active on te CSA orking Group M421 and CSA C22.2 #96. He is also a member of te Electrical Electronic Manufacturers Association of Canada and an alternate to ICEA. In addition, e is a member of te IEEE orking group on electrical submersible pump cable. Marcus. Duram (S 64-M 76-SM 82) received te B.S. degree in electrical engineering from Louisiana Tecnical University, Ruston, te M.E. degree in engineering systems from te University of Tulsa, Tulsa, OK, and te P.D. degree in electrical engineering from Oklaoma State University, Stillater. He is te Principal Engineer of Teay Corp., Tulsa, OK, ic is an engineering, management, and operations group tat conducts training, develops computer systems, and provides design and failure analysis of facilities and electrical installations. He is also an associate professor at te University of Tulsa, specializing in microcomputer applications and electrical/mecanical energy systems. He as developed a broad spectrum of electrical and facilities projects for bot U.S. and international companies. Based on is extensive background, e as become a recognized autor o as publised numerous papers, articles, and manuals and as conducted training in suc diverse topics as electrical poer design, management, and microcomputer applications. Dr. Duram is a registered Professional Engineer, a state licensed electrical contractor, and a FCC licensed radiotelepone engineer. Professional affiliations include member of te Society of Petroleum Engineers. He as served on and been Cairman of many committees and standards groups itin te IEEE, SPE, and API. Honorary affiliations include Pi Kapp Pi, Tau Beta Pi, and Eta Kappa Nu.