Slip Calculation of Rotational Speed of Electrical Submersible Progressive Cavity Pumps Desheng Zhou, SPE, Hong Yuan, SPE, IHS Inc.

Transcription

1 SPE Slip Calculation o Rotational Spee o Electrical Submerible Progreive Cavity Pump Deheng Zhou, SPE, Hong Yuan, SPE, IHS Inc. Copyright 2008, Society o Petroleum Engineer Thi paper wa prepare or preentation at the 2008 SPE Progreing Cavity Pump Conerence hel in Houton, Texa, U.S.A., April Thi paper wa electe or preentation by an SPE program committee ollowing review o inormation containe in an abtract ubmitte by the author(). Content o the paper have not been reviewe by the Society o Petroleum Engineer an are ubject to correction by the author(). The material oe not necearily relect any poition o the Society o Petroleum Engineer, it oicer, or member. Electronic reprouction, itribution, or torage o any part o thi paper without the written conent o the Society o Petroleum Engineer i prohibite. Permiion to reprouce in print i retricte to an abtract o not more than 300 wor; illutration may not be copie. The abtract mut contain conpicuou acknowlegment o SPE copyright. Abtract Progreive cavity pump (PCP) are uually riven at urace through ucker ro. Due to the hear trength o ucker ro an the wear o the ro an tubing, the urace rive ytem limit it application in prouction rate an well epth, an in eviate an horizontal well. Intea o uing ucker ro to tranmit riving torque rom urace to pump, bottom riving PCP aembly et electric ubmerible motor below PCP to rive the pump irectly. Electric ubmerible motor or PCP are three phae, quirrel cage, inuction motor. Motor pee i controlle by it wining pole. ominal motor pee wiely ue are 3500 RPM or two-pole motor an 1700 RPM or our-pole motor. Thi paper preent impliie correlation by uing the nominal motor pee in the eign an analyi o bottom riving PCP well. The impliie correlation o not account or the eect o motor pee lip. Actually, motor output pee epen on loaing power on the motor. Loaing power i the power require by a PCP an it aociate equipment to lit well lui to urace. Thi paper preent the power conumption o each part in the bottom rive aembly, an the metho o calculating motor lip rom motor pee perormance an calculate total require power. Alo preente i the eect o requency on motor pee. Finally preente are a moel to eign motor requency with motor lip an an iteration algorithm to etermine prouction rate at given requency. Thi paper clariie the concept o volumetric, brake, mechanical, hyraulic, an lip power aociate with PCP pumping. It alo ierentiate motor output nominal, no-loa, an ull-loa pee, an the output pee at loa actor, at tanar requency, an at eign requencie. Introuction A progreive cavity pump (PCP) i a pecial type o rotary poitive iplacement pump. It wa irt introuce in petroleum engineering a an artiicial lit metho in A PCP ha many avantage to other artiicial lit metho, uch a lower invetment, broaer application to lui mixture, le maintenance, an higher eiciency. It i becoming a popular lit tool an, or ome well, the bet choice rom all artiicial lit metho. The PCP ue in artiicial lit i a ingle lobe pump that conit o a ingle external helical rotor turning eccentrically inie a ouble internal helical tator. The pecial PCP tructure make pumping lui low almot axially, moothly an continuouly, which reuce lui agitation an churning an thereore reuce lui emulion an oli eroion. Unlike a centriugal pump, lui vicoity will not egrae the pump hea o a PCP, but increae pumping volumetric eiciency. Since a PCP i a poitive iplacement pump, it oen t have the problem o ga lock theoretically. However, ue to temperature increae rom ga compreion, PCP can only hanle high ga lug in a hort time. Due to the eature o moving eal line along PCP axi, cale oe not normally epoit in a PCP. PCP have relatively low inertia in their rotating part, an thereore have a reliable working lie. Traitionally, PCP in well are riven rom the urace by a wellhea riving aembly. The tator o a PCP run into a well at the en o tubing tring, an PCP rotor run into the tubing tring at the bottom o ucker ro. Unlike or a beam pump well where the ucker ro move up an own, the ucker ro in a PCP well rotate at wellhea an tranmit torque ownwar to rive the rotor in the till tator. Only the PCP an ucker ro are et in a wellbore or a wellhea riving PCP ytem, other equipment are intalle on the urace. Thereore, the ytem ha goo reliability an long working lie. The urace equipment can be maintaine eaily without hutting the well in or a long time.

2 2 SPE However, the wellhea riving ytem ha ome limitation ue to it ucker ro. A ucker ro ha a critical torque trength, above which the ro may be broken. The require torque to rotate a PCP i proportional to prouction rate; hence wellhea riving ha a limitation in lui prouction capacity. The require torque i alo proportional to total ynamic hea, thereore wellhea riving ha a limitation in pumping epth. Another limitation i tubing ize. Since the ro i et in tubing, reaonable tubing ize i neee to maintain a ro-tubing annular or lui low. Due to lui low over ucker ro, there i an extra riction preure lo or the wellhea riving ytem. In aition, or the wear between ucker ro an tubing, tubing lie may be aecte. The wear o ro an tubing tring retrict the application o wellhea riving PCP aembly in eviate an horizontal well epecially. In 1990, bottom riving PCP wa introuce to get ri o ucker ro. The PCP i riven by an electric ubmerible motor et below the PCP. The motor can generate enough torque an thu the bottom riving ytem can prouce larger amount o lui an work in eeper well. Without the riction lo over ucker ro, the bottom riving ytem improve ytem eiciency. Without the contact between ucker ro an tubing tring, bottom riving PCP oen't have problem o ro broken an tubing wearing, an it can be operate in eviate an horizontal well. A bottom riving PCP ytem conit o electric ubmerible motor, protector, gear reucer an lex hat rive, pump intake an PCP. A rotary ownhole eparator may alo be intalle below pump intake to eparate ga. The rotational pee o a PCP can be calculate rom require prouction rate, pump volumetric perormance, an the require hea rom well inlow an outlow perormance. For a bottom riving ytem, motor operating requency houl be eigne to rive the pump at it require pee. Thi paper preent impliie moel to eign the require requency an to analyze prouction rate. The total require horepower to the motor an the uing o motor pee perormance curve are icue in etail. Motor output pee will be reuce when there i a loa on it. The pee reuction i motor lip. Thi paper preent moel to calculate the lip, an how how to ue the lip in eigning the require requency. Alo preente in the paper i the calculation o PCP prouction rate at a given requency. Thi i ueul in the analyi o PCP well. At a given requency, the motor output pee epen on it brake horepower. The horepower i aecte mainly by the prouction rate, an the prouction rate etermine require motor pee. Thereore, iteration metho i neee to olve the prouction rate or a given requency. Bottom Driving PCP Sytem an Total Horepower Bottom riving PCP ytem conit o electric ubmerible motor, protector, gear reucer, lex rive, intake an PCP. The PCP i riven rom it bottom in a counter clockwie irection. Each part in the ytem will conume ome horepower uring operation an the total horepower i the key actor to etermine motor output pee. Alo, the analyi o power conumption i helpul in improving ytem eiciency. PCP Require Horepower. When talking about the horepower o a PCP, oten mentione are brake horepower, hyraulic horepower, eective horepower, lip horepower an mechanical horepower (Karaik et al, 1991). It i ueul to itinguih them or pump eign an optimization. The brake horepower, b, i the horepower require to rive a PCP, which i the um o hyraulic horepower, h, an mechanical horepower, m. The hyraulic power i the work one to pump the lui rom pump intake preure to the icharge preure. ote that the work i one on all the pumping lui, incluing leakage an elivere lui. The hyraulic horepower i expree a, h qtδp =. (1) Where h i in hp, q t i the theoretical iplacement rate o a PCP, B/D, Δp i the ierential preure between pump intake an icharge, pi. The eective horepower o a PCP i the work one on pumping the actual elivere lui, an it oe not inclue the volumetric lip. It can be calculate by replacing the theoretical low rate in Eq. 1 by the actual low rate at pump icharge, q a. The horepower conume by the lip lui can be calculate by uing the lip rate, q, in Eq. 1 a e qaδp = (2) qδp = Where e an are the eective horepower an lip horepower repectively, an both are in hp, q a an q are the actual

3 SPE pumping lui meaure at pump icharge an the volumetric lip rate, both are in B/D. The hyraulic horepower i actually the total o the eective horepower an lip horepower. = +. (3) h e The hyraulic horepower i inepenent o lui vicoity, a hown in Eq. 1, an i a unction o only the pump imenion, rotational pee, the lip, an the ierential preure. The mechanical horepower repreent the internal power loe in a PCP. It conit o riction loe an lui hearing loe. The riction loe are the loe rom the riction o part to part an lui to part, which inclue all the power to overcome the riction o all moving part an the riction to the lui low. The hearing loe come rom the hearing action in the lui itel. They are aecte by rotor rotational pee, pump cavity geometry, an lui hearing characteritic (ewtonian or non-ewtonian behavior). The pump volumetric eiciency i eine a the ratio o actual elivere rate to theoretical low rate, an i expree a (Zhou an Yuan, 2008) E v q q a t = =. (4) t q q q t Where, E v i the pump volumetric eiciency, q a, q t an q are the actual elivere rate, theoretical iplacement rate an volumetric lip rate repectively. The mechanical eiciency i the ratio o hyraulic horepower to the brake horepower o the pump, h E m =. (5) b The pump eiciency o a PCP, E p, i the ratio o the eective horepower, e, to the brake horepower, b. e E p =. (6) b Multiplying the hyraulic horepower on the numerator an enominator o Eq. 6, an ubtituting Eq. 1 an 2 into Eq. 4 yiel E e h p = = Ev Em. (7) h b Thereore, the eiciency o a PCP i the prouct o it volumetric eiciency an mechanical eiciency. The volumetric eiciency relect the volumetric lip an the mechanical eiciency relect the loe ue to riction an hearing action. Subtituting the eective horepower in Eq. 2 into Eq. 6 an olving or the brake horepower yiel b q Δp a =. (8) 58766E p Changing the ierential preure in Eq. 8 to total ynamic hea yiel q Hγ a b =. (9) 136,000E p

4 4 SPE Subtituting pump eiciency in Eq. 7 into Eq. 9 yiel the pump brake horepower a b q Hγ t =. (10) 136,000E m Where E m i the mechanical eiciency that epen on lui vicoity, rotational pee, an the it between the rotor an the tator. q t i in B/D, H i the total ynamic hea in t, γ i the peciic gravity o the lui, an the brake horepower b i in hp. The calculation o the mechanical eiciency i rather complex, an normally tet value rom manuacturer are ue. Gear Reucer an Flex Shat. For the reaon o working lie an eiciency, a PCP ha a maximum operating pee (or intance, 500 revolution per minute (RPM)) in iel application. At 60 Hz, normally ue output pee o two or our-pole motor are approximately 3500 RPM or 1700 RPM repectively. The motor pee houl be reuce to a value below the maximum pee o the PCP. Gear reucer i ue to reuce the motor pee own to an acceptable range or the PCP. There are many type o gear reucer to chooe rom epening on gear reuction ratio. The mot eicient combination in petroleum inutry i electing a gear reucer with 9 : 1 gear ratio or a two-pole motor or 4 : 1 gear ratio or a our-pole motor. The rive pee i 389 RPM ater the 9 : 1 reuction, an 425 RPM ater the 4 : 1 reuction. Gear reucer may be equippe with thrut bearing to hanle the own thrut orce rom the PCP. Gear reucer may alo inclue upthrut bearing to keep the rotor in the tator when the rotor rotate in a revere irection. The rotor o a PCP rotate eccentrically. A lex hat i ue between the PCP an the gear reucer to convert the concentric rotation o the gear reucer to the eccentric rotation o the rotor. Seal are et at the lex hat to prevent well lui rom the gear reucer. The eiciency o the gear reucer i mainly aecte by gear reuction ratio, gear mehe (ingle or ouble reuction gear), input rotational pee, tooth geometry, an own thrut orce on the thrut bearing. Among them, the reuction ratio i the key actor. The horepower conumption or eiciency o a gear reucer an lex hat aembly i tet reult rom manuacturer. Generally, the gear reucer an lex hat aembly ha the eiciency o 0.98 or ingle planetary reuction, an 0.96 or ouble planetary reuction. Protector. Protector i et between gear reucer an electric ubmerible motor to provie eal or the gear an the motor rom well lui. It top chamber contain gear oil an it bottom chamber contain motor oil. The protector allow the motor oil an gear oil to expan or contract a temperature an preure varie in ownhole conition. It alo equalize internal motor preure an gear preure with the wellbore preure. The protector may be equippe with thrut bearing to aborb the own thrut orce rom the PCP. The horepower conumption o a protector epen on it eal type, protector ize, an own thrut orce or eal with thrut bearing. Manuacturer provie correlation to calculate the horepower conumption in a polynomial orm bae on their tet ata. The power conumption i mall in comparing with the hyraulic power. Generally, the horepower conumption o a protector i in the range o 0.1 hp to 2 hp. An etimation or the horepower conumption i ptr = 0.5 hp. Motor Frequency Deign Simpliie Moel. Electric ubmerible motor or PCP are generally three phae, quirrel cage, inuction motor. The motor have magnetic pole in motor houing. A pole i a bunch o woun wire an alo calle wining. The number o pole in a motor control it rotational pee. The more pole a motor ha, the lower the pee it rotate. The electric ubmerible motor in petroleum engineering are two, our, or ix-pole motor. At 60 Hz an without loa, a two-pole motor turn 3600 RPM, a our-pole motor rotate 1800 RPM, an a ix-pole motor ha the pee o 1200 RPM. At 60 Hz an ull loa, motor pee i approximately 1700 RPM or our-pole motor an 3500 RPM or two-pole motor. The 1700 RPM or our-pole motor an 3500 RPM or two-pole motor are wiely ue an are reerre to a nominal pee in thi paper. In petroleum prouction engineering, motor erie are 375, 400, 456, 540, an 562, which come rom the 100 time o motor' outie iameter in inche. For a 562 erie motor, or example, the motor outie iameter i 5.62 inche. For a eire prouction rate in a PCP well, the calculate eign pee o the PCP may not be the output pee rom the gear reucer. A variable pee control unit at urace i ue to vary the motor requency to make the output pee equal the eign PCP pee. Approximately, motor pee i proportional to the requency. The relationhip o motor requency with the motor nominal pee at tanar requency o 60 Hz can be expree a, n mtr mtr =. (11) 60

5 SPE Where n mtr-, RPM, i the output pee o a motor at the eign requency o Hz. mtr i the nominal pee o the motor at ull loa, which i 3500 RPM or two-pole motor or 1700 RPM or our-pole motor. For a gear reuction ratio o gr, the relationhip between motor output pee an pump pee i n = n mtr pcp gr. (12) For example, or a 9 : 1 gear reucer at 60 Hz, the pump pee i 389 RPM. Subtituting Eq. 12 into Eq. 11 an olving or the requency yiel, 60n pcp gr =. (13) mtr Ater electing a gear reucer, the only variable in Eq. 13 i the pump pee. For a eire prouction rate, the eign pee o a PCP can be calculate rom PCP volumetric pump perormance an well perormance a preente by Zhou an Yuan (2008). Once the pump pee i obtaine, Eq. 13 i ue to calculate the eign requency or the motor. For example, i the eign pee o a pump i 350 RPM, the eign requency i 60*350*9/3500 = 54 Hz. The metho to etermine motor requency rom Eq. 13 i imple to ue. In the moel, the motor nominal pee at ull loa, 3500 RPM or two-pole motor or 1700 RPM or our-pole motor, i ue without the knowlege o motor characteritic or perormance. Eq. 13 work or all erie o motor. However, the motor nominal pee at ull loa i jut an approximate value. Each motor ha it own pee perormance. For rigorou calculation, motor perormance nee to be analyze. Motor Perormance. A motor ha characteritic value o nameplate horepower, nameplate voltage an nameplate current given by motor manuacturer. In iel application, epening on the loa on the motor, motor output horepower, voltage an current vary, which are not the ame a the nameplate value. Motor manuacturer tet their motor perormance at tanar requency, which i 60 Hz or 50 Hz. Fig. 1 how a typical motor perormance curve or a two-pole motor at 60 Hz. The motor ha nameplate horepower o 20 hp, nameplate voltage o 770 volt an nameplate current o 17 ampere. In the igure, the eiciency an the power actor are in percentage. The current i expree a the percentage o motor nameplate current. The eiciency, power actor, an the percentage o nameplate current all ue the let ie vertical axi. The right ie vertical axi i ue or motor pee. The horizontal axi i the loa actor in percentage. A hown in Fig. 1, the motor eiciency, power actor, current, an rotational pee vary with the loa actor. Loa actor i the ratio o the require horepower on the motor, to motor' nameplate power, rq LF =. (14) np Where rq i the require horepower on the motor, np i the nameplate horepower o the motor. A hown in Fig. 1, the rotational pee i 3600 RPM at the loa actor o zero, an 3469 RPM at ull loa (loa actor equal one). The pee 3500 RPM correpon to a loa actor o 0.8 or the peciic motor. Thereore, at ull loa, the motor output pee i not a contant o 3500 RPM. The nominal pee, 3500 RPM here, i jut an approximation. Motor pee ecreae a loa actor increae. The maximum pee o a motor i at no-loa, which i calculate a, 120 / = pole. (15) Where i the motor pee at no-loa, RPM, i the tanar requency, Hz, pole i the number o pole o the motor. From Eq. 15, at 60 Hz, the no-loa pee,, i 3600 RPM or a two-pole motor an 1800 RPM or a our-pole motor. The motor no-loa pee i proportional to the requency on it an i expree a / =. (16)

6 6 SPE Where i the motor no-loa pee at eign requency. Motor actual pee at any loa i le than it maximum value. The ierence i calle the pee lip o the motor. The larger the loa on the motor i, the larger the motor lip. I a motor output pee i n mtr- at tanar requency, the motor pee lip S, RPM, i S = n mtr. (17) Subtituting Eq. 15 into Eq. 17 an olving or motor pee yiel n = 120 * pole S. (18) mtr / Eq. 17 i the correlation to calculate the motor pee lip. The motor pee i etermine rom motor pee perormance curve at a given loa actor. Loa actor i eine in Eq. 14 an the control actor to etermine the loa actor i the loa, the total require horepower, an the nameplate horepower o the motor. For a bottom riving PCP, the total require horepower i the um o the pump brake horepower, the power conumption by the gear reucer an lex hat, an the power lo ue to the protector. When a ownhole eparator i intalle, it horepower conumption houl alo be ae to obtain the total require horepower or the motor. + rq = b + gr& l ptr. (19) Where b i the brake horepower o the pump, gr&l i the horepower conume by the gear reucer an lex hat, ptr i the protector conumption. Once the total require horepower i calculate, Eq. 14 i ue to etermine the loa actor or the electe motor, an the actual motor pee at the loa i calculate rom the motor' pee perormance curve. Motor Frequency Moel with Slip. The pump eign pee n pcp i etermine uring PCP eign rom require prouction rate, lui propertie, an well ytem perormance. Once the PCP pee i calculate, the require pee or the motor can be calculate rom Eq. 12. However, the motor output pee at tanar requency may not equal the require pee. The requency on the motor houl be ajute to make the motor output pee match the require motor pee. For the require prouction rate, lui propertie an well conition, the total require horepower can be calculate rom Eq. 19. The total require horepower i the power at the eign requency, at which the motor output pee matche the require pee rom the PCP. The total require horepower i expree a rq- to emphaize that it i the power at eign requency. Motor perormance curve (a hown in Fig. 1) are tet reult at tanar requency (60 Hz or 50 Hz). The total require horepower at eign requency houl be converte to the horepower at the tanar requency. rq = rq. (20) Where rq- i the total require horepower at tanar requency. The loa actor at tanar requency, LF, can be calculate rom Eq. 14 a, LF rq =. (21) np Uing the calculate loa actor at tanar requency, the motor output pee at tanar requency, n mtr-, i calculate rom the motor pee perormance curve. Subtituting the calculate motor pee into Eq. 17, the pee lip, S, at the loa actor i etermine. Motor output pee at eign requency i the prouct o pump eign pee an gear reuction ratio. Motor no-loa

7 SPE pee at eign requency i = npcpgr S. (22) + Subtituting Eq. 22 into Eq. 16 an olving or eign requency yiel, ( n + S) pcp gr =. (23) Thi i the correlation to calculate the eign requency or a eire prouction rate. Comparing with the impliie eign moel in Eq. 13, the impliie moel oen t contain the pee lip an it ue the nominal motor pee intea o the motor no-loa pee at tanar requency. For intance, or two-pole motor at 60 Hz, Eq. 23 i reuce to 60( npcp gr + S) =, (24) 3600 an the impliie moel Eq. 13 i 60 gr npcp =. (25) 3500 Motor Frequency Analyi The above ection preent the metho or calculating motor eign requency at a given pump pee. One may nee to etermine the pump pee, or the prouction rate, or a given motor requency. Thi i ueul in analyzing PCP well. A impliie moel i erive by olving Eq. 13 or pump pee. n pcp mtr =. (26) 60 gr Eq. 26 i a impliie analyi moel can be ue to calculate pump pee at a given requency. The moel i eay to ue without the knowlege o motor peciic perormance. Once the pump pee i obtaine, the prouction rate o the well can be etermine rom the pee, lui propertie an well inlow an outlow perormance (Zhou an Yuan, 2008). However, a icue above, ue to motor pee lip, the actual motor pee i not the nominal pee o 3500 RPM or two-pole motor or 1700 RPM or our-pole motor at 60 Hz. Motor actual output pee i a unction o loa actor a hown in Fig. 1. The loa actor epen on the total require horepower on the motor. The rigorou moel or analyzing the eect o requency can be erive rom Eq. 23. n pcp 1 = S. (27) gr To calculate the pump pee rom Eq. 27 at a given requency, motor pee lip houl be etermine irt. However, the pee lip epen on the pump pee. The pee lip i etermine by the loa actor, an the loa actor i controlle by the total require horepower on the motor. The total require horepower i etermine by Eq. 19. The pump brake horepower take the major part in the total horepower. A hown in Eq. 10, the brake horepower varie with pump iplacement rate. The iplacement rate i proportional to pump rotational pee. That i, to calculate the pee lip, pump pee houl be known. Thereore, iteration calculation i neee to olve Eq. 27. The algorithm to etermine pump rotational pee (or prouction rate) at a given motor requency i: 1. Ue Eq. 26 to etimate an initial pump pee. For example, or a two-pole motor with a 9: 1 reucer at 54 Hz, the

8 8 SPE pump rotational pee i 350 RPM. 2. For the pump pee, calculate the prouction lui rate through the pump uing the metho o Zhou an Yuan (2008). 3. Calculate the hyraulic horepower an the total horepower rom Eq. 19 at the pump pee an prouction lui rate. 4. Uing the calculate total horepower, calculate the loa actor at tanar requency rom Eq. 20 an 21. Calculate motor pee lip rom Eq. 17 an calculate the motor output pee rom motor pee perormance curve. 5. Solve a new pump pee rom Eq. 27 uing the calculate pee lip. I the ierence o the new pump pee an the initial pump pee i in an acceptable range, the new pump pee i the olution. Otherwie, 6. Ue the new pump pee a the initial pump pee an continue the iteration rom tep 2. Concluion Thi paper preent impliie moel an rigorou moel to eign motor requency at a given pump pee, an to analyze pump pee or prouction rate at a given motor requency in a bottom riving PCP ytem. The major ierence between the impliie an the rigorou moel i that the impliie moel neglect the lip o motor pee. Since motor pee varie with it loa, the impliie moel only give an approximate relationhip. The impliie moel ue the nominal pee o 3500 RPM or two-pole motor an 1700 RPM or our-pole motor. The impliie moel i eay to ue ince the knowlege o motor peciic perormance i not require. The rigorou moel require calculating o total require horepower an uing o motor perormance curve. It i accurate but a computer program i neee to complete the calculation. Pump pee epen on motor lip an the motor lip i etermine by the pump pee. An iteration algorithm i employe to analyzing the eect o motor requency on the pump pee or prouction rate. omenclature E m E p E v H b e gr&l h ptr rq rq- rq- np LF LF gr mtr pole n mtr- n mtr- n pcp q a q q t S γ Δp = mechanical eiciency, imenionle = pump eiciency, imenionle = volumetric eiciency, imenionle = eign requency, Hz = tanar requency (60 or 50 ), Hz = total ynamic hea, t = brake horepower, hp = eective horepower, hp = horepower conumption o gear reucer an lex hat rive, hp = hyraulic horepower, hp = protector horepower conumption, hp = total require horepower, hp = total require horepower at tanar requency, hp = total require horepower at eign requency, hp = lip horepower, hp = motor nameplate horepower, hp = motor loa actor, imenionle = motor loa actor at tanar requency, imenionle = motor no-loa pee at eign requency, RPM = gear reuction ratio, imenionle = nominal motor pee (3500 or two-pole motor or 1700 or our-pole motor at 60 Hz), RPM = number o motor pole = motor no-loa pee at tanar requency (3600 or two-pole or 1800 or our-pole motor at 60 Hz), RPM = motor output pee at eign requency, RPM = motor output pee at tanar requency, RPM = PCP pump rotational pee, RPM = actual pump rate, B/D = volumetric lip rate, B/D = theoretical PCP iplacement, B/D = motor lip, RPM = peciic gravity = ierential preure rom pump intake to icharge, pi Acknowlegment The author woul like to thank IHS IC. or permiion to publih thi paper.

9 SPE Reerence 1. Karaik, I. J., Meina, J. P., Cooper, P., Heal, C. C., 1991, Pump Hanbook, Thir Eition, McGraw-Hill. 2. Zhou, Deheng, Yuan, Hong: Deign o Progreive Cavity Pump Well, Paper SPE to be preente at the 2008 SPE Progreing Cavity Pump Conerence, Houton, TX, April. SI Metric Converion Factor bbl hp pi E-01 = m3 E-01 = kw E+00 = kpa *Converion actor i exact %P Current 3600 Eiciency Percent Motor Spee, RPM Spee Power Factor Loa Factor, % 3400 Fig. 1 Motor perormance with loa actor.