A METHOD FOR MEASUREMENT OF HYDRAULIC LOSSES IN CENTRIFUGAL PUMPS

Transcription

1 A METHOD FOR MEASUREMENT OF HYDRAULIC LOSSES IN CENTRIFUGAL PUMPS Cleber Sandi Xiene State Univerity of Capina UNICAMP-FEM-DEP Cx.P Capina, SP, Brazil Antonio Carlo Bannwart State Univerity of Capina UNICAMP-FEM-DEP Cx.P Capina, SP, Brazil Fernando A. França State Univerity of Capina UNICAMP-FEM-DE Cx.P Capina, SP, Brazil Valdir Eteva PETROBRAS E&P Rio de Janeiro, RJ, Brazil Abtract. The election of a centrifugal pup for an ESSP application depend on any factor, including fluid propertie uch a vicoity and denity. When a centrifugal pup i handling a vicou fluid - uch a heavy oil - it perforance i ipaired in coparion to operation with light oil due to increaed frictional loe. There are very few publihed data available to evaluate the agnitude of vicou effect. Uually the perforance decay for operation with vicou fluid i etiated by ean of epirical correction factor applicable to flow rate, head and efficiency. However, large dicrepancie between actual and predicted perforance have been oberved in practice. The current work ha a objective to develop a ethod for eaureent and evaluation of the loe in centrifugal pup. Thi i carried out by eploying one-dienional balance equation for the ingle-phae flow into the pup. Focu i directed to the hydraulic loe, which include frictional, recirculation and hock loe. Meaureent perfored with water in a two-tage pup at everal Reynold nuber and rotation peed are preented and dicued. Keyword: Petroleu engineering, heavy oil, centrifugal pup, electrical uberible pup, vicou effect.. Introduction The viability of heavy oil production in offhore deep and ultra-deep water field depend upon the developent and iproveent of artificial lift ethod, aong which the Electrical Suberible Subarine Pup (ESSP) ha been deontrated to be an iportant ethod for high flow rate well. The election of a centrifugal pup for ue in an ESSP application depend, of coure, on it perforance paraeter. Typical perforance curve are hown in Fig., which illutrate the relationhip between pup head, pup efficiency and break horepower, with the liquid flow rate. The anufacturer uually provide thee experientally deterined curve uing water. The perforance curve are extreely dependent upon the pup ipeller and diffuer geoetric deign. A ketched in Fig., a typical ingle-tage pup conit of an ipeller rotating within a caing. The fluid enter axially through the eye of the caing, it i caught up in the ipeller blade and whirled tangentially and radially outward until it leave through all circuferential part of the ipeller into the diffuer part of the caing. The fluid gain both velocity and preure while paing through the ipeller. The diffuer or croll ection of the caing decelerate the flow and further increae the preure. The top view of a typical ipeller i illutrated in Fig. 3. A generic ketch of a radial ipeller i hown in Fig. 4. The ipeller rotate clockwie with the pup haft angular velocity, ω. The diffuer i tationary. The inide circle i the entrance of the ipeller, or dicharge of a diffuer. The outide circle i the dicharge of the ipeller, or entrance of a diffuer. The ipeller or diffuer i divided into everal channel by curve blade. The angle β between the outward blade tangent and the peripheral line oppoing the rotating direction i called the blade angle at that location. By convention, the ubcript refer to entrance, while ubcribe refer to dicharge. Therefore, for the ipeller hown in Fig. 4, β i the ipeller entrance blade angle and β i the ipeller dicharge blade angle. The dahed curve at the iddle of the channel i called the trealine of fluid, if the flow inide the channel i aued to be one-dienional. Perforance curve baed on water tet upply realitic value to efficiency, head and capacity (flow rate) when the fluid ha a vicoity that i about the ae a water ( cp). In any cae, however, the liquid puped (uch a vicou oil, ugar ollae, etc) ay be ore vicou. In thee cae, pup perforance coniderably change fro behavior hown by the actual eaureent with water. Vicou liquid caue greater hydraulic loe in the pup, leading to lower puping head and efficiency and greater power. The puping head and puping efficiency curve fall below the correponding water-perforance curve, while the hut-off head point reain the ae, regardle the vicoity.

2 The correction factor publihed by the Hydraulic Intitute (HI) are widely ued to predict the perforance of a centrifugal pup with vicou fluid. When the characteritic for puping water i known, thoe for a vicou liquid can be deterined by ultiplying the water value by correction factor to head, efficiency and capacity. The correction factor provide by HI are a concluion baed on tet of conventional centrifugal pup with petroleu oil. Neverthele, in any cae, the correction ethod of HI give a peiitic prediction of pup perforance and therefore treendou over izing that can take to an ipractical project. Although fluid vicoity i very deciive on centrifugal pup application, there are few publication about centrifugal pup handling high-vicoity fluid. Wen-Guang Li (00) preent a ethod for deterining oe paraeter, uch a lip factor, hydraulic, echanical and voluetric efficiencie baed on the experiental perforance of centrifugal oil pup. The invetigation wa perfored with a ingle-tage centrifugal pup handling fluid with kineatical vicoity range aong cst and 55 cst. Coparion between prediction and tet data were done. The experiental reult deontrated that echanical and hydraulic efficiencie decreae a the vicoity of liquid puped increae, in contrat with voluetric efficiency that ha nothing to do with vicoity variation. Recently, Gülich (003) revealed that dik friction and friction loe in the hydraulic paage of the pup are the doinating factor. In thee invetigation a atheatical odel baed on an analyi of the vicou loe in the centrifugal pup wa developed. However, it i iportant to point out that the reearch group cited previouly preent correlation valid for the pecific pup deign teted. In the preent work, a laboratory cale apparatu wa ued to invetigate and to forulate a generic odel for fluid flow through centrifugal pup. Figure : Typical centrifugal pup perforance at contant ipeller rotation peed (White, 994). Figure : Typical centrifugal pup Figure 3: Ipeller top view Figure 4: Sketch of a radial ipeller geoetry. One-dienional approach.. Fluid velocity and central trealine The velocity field inide the channel i three dienional and very coplexe. In thi tudy, one-dienional flow along a channel i aued baed on continuity, linear oentu, angular oentu and energy equation. The fluid

3 ρ particle flow along a trealine a hown in Fig. 5. The relative velocity, w, between the fluid and the channel i tangent to the central trealine. The flow area i noral to the trealine. The fluid flow fro the entrance to the dicharge of the ipeller along each curved channel. During thi operation, the ipeller i rotating around the haft axi, and any point on the ipeller ha a peripheral velocity, u given by, u = ω r () where ω i the angular velocity of the rotating haft or ipeller in the clockwie direction, and r i the radial poition of a point on the ipeller. The fluid particle ha abolute flow velocity, V, that i the vectorial u of the relative velocity of the flow and the peripheral velocity, V = w + u () The diagra for the velocity vector i hown in Fig. 4. Thi i called the velocity triangle diagra. The angle β i between w i and the negative of u i, and in ideal flow cae the ae a the angle between the tangent to the ipeller channel and a line in the direction of otion of the vane. V ni and V ti are, repectively, the radial and tangential coponent of the abolute velocity, V. Relationhip between thee velocitie and their coponent can be obtained fro iple geoetric relation. For ideal, one-dienional, one-phae flow through a pup, the velocity triangle are a function of the pup geoetry, angular ipeller velocity and the a flow rate. For tead-tate, one dienional and incopreible flow, the equation of continuity, linear oentu, angular oentu and energy applied between the inlet and outlet of the ipeller reduce to (ee Noenclature ection): Ma Conervation Equation Q = π r = (3) b Vn π r b Vn Linear Moentu Conervation Equation p w + + z ρg g u p w + + z g ρg g u τ wswd = + g ρ g A hi,local (4) where h i,local tand for the local irreverible loe that can be aociated ainly with flow eparation. Angular Moentu Conervation Equation ( V r V ) T T = ρ Q r (5) Energy Conervation Equation t t p V p V H = h = h f z z ρg g ρg g (6) A relationhip aong Eq. (4-6) appear when Eq. (5) i ultiplied by ω / ( ρ Q g). The following reult i obtained: h uvt uvt = (7) g ( T T ) ω where h = i the head upplied by the pup. Additional inight i gained by rewriting thee relation in Qg another for when velocity triangle i applied: ( V + u w ) uv t = (8) Replacing Eq. (8) into Eq. (7) read: h [( V + u w ) ( V + u w )] = (9) g Inerting Eq. (9) into (6) give the following reult:

4 p w + ρg g + z u p w + g ρg g + z u = h g f (0) Equation (0) and (4) becoe equivalent if: τ ws wd h f = + h ρga i,local () According to Stephanoff (957) the hydraulic loe are, in a one-dienional approach, not only the leat well known, but alo the ot iportant. Hydraulic loe can be roughly categorized a friction, eddy and eparation loe caued by change in direction and agnitude of the velocity (including the hock and diffuion lo). Thu, h f. ut include all irreveribilitie aociated with wall friction, recirculation and hock of the flow through the ipeller. In thi work, Eq. (0) i ued to experientally deterine h f. The theoretical head, h, upplied to the fluid can be expreed by a different verion of Eq. (7), i.e.: h = [ u ( u Vn cot β ) u( u Vn cot β )] = [ u ( u uvn cot β ) uvn cotα] () g g The net head, H, reult fro the difference h - h f. For copletene, we introduce the overall efficiency, η, which i the ratio of the power delivered by the pup to the fluid to the power aborbed by the pup. Thi paraeter i baically copoed of three ter: echanical, hydraulic and voluetric efficiencie. If h f i known, then the hydraulic efficiency can be obtained a: H h f η h = = (3) h h Beide the head loe, there are capacity loe known a leakage loe. The ratio between the capacity available at the pup dicharge, Q, and that paing through the ipeller, Q+Q L, i known a voluetric efficiency: Q η V = (4) Q + Q L Mechanical loe include thoe due to the tuffing box and thoe at the bearing. Thee loe, according to Stephanoff (957), are relatively all copared to other loe and arie due to the deign of the ball bearing and the tuffing box. They can be related to the echanical efficiency by: η W& W& = W& = ( T T ) ω T = T ω T (5) The relationhip aong the partial efficiencie and the overall efficiency can be obtained fro: ρqgh η = = ηη hη v (6) ω T 3. Experiental work The experiental reult preented in thi paper were obtained in the Multilab Facility at the School of Mechanical Engineering of UNICAMP. The experiental apparatu i illutrated in Fig. 5. The cloed-loop circuit i copoed by: a -tage tet pup Ita / upplied with an 5 hp electric otor and haft peed of 00 rp, a booter ingletage pup Ita provided with an 5 hp electric otor and haft peed of 750 rp, a haft peed controller for booter and tet pup, a digital torque eter connected between electric otor and tet pup axi, preure enor at pecific point of the tet pup, agnetic and vortex flow eter, globe and phere valve for flow control, and a 5 3 capacity reervoir. Table lit the geoetric data of the tet pup ipeller. Perforance data were recorded uing tap water. Flow rate, uction preure, t tage exit preure, dicharge preure, haft torque, and haft peed were eaured. Fig. 6 preent cheatically the location of the preure enor into the pup. In the experiental procedure the booter pup worked with it axiu rotation fixed in 750 rp. Shaft peed of 600, 700, 800, 900 and 000 rp were etablihed to tet pup by ean haft peed controller. For each one of thee rotation, at leat ten data were collected between hut off and axiu flow rate (38 3 /h) for

5 each of the characteritic curve. Vortex and agnetic eter controlled by ean of a phere valve et in the dicharge line were ued for flow rate eaureent. Thee data were ued to deterine the net head of each ipeller, the pup net head, the input haft power and the head lo between inlet and outlet of each ipeller, for each tet run. Figure 5: Sketch of cloed circuit Table : Input geoetric data for the ipeller t ipeller nd ipeller Nuber of blade (N) 8 8 Blade thickne (δ) 3 4 Channel width at inlet (b ) Ipeller entrance diaeter (D ) 80 Ipeller dicharge diaeter (D ) Inlet blade anlge (β) 0 o 0 o Oultet blade angle (β) 35 o 35 o 4. Reult Figure 6: Point where preure enor were placed into the pup In order to ae the propoed eaureent ethod, the net pup head, H, i plotted againt the flow rate in Fig. 7, for everal pup rotation peed. Thi i, perhap, the ot typical characteritic curve of centrifugal pup. It can be oberved that the net head increae with increaing pup peed and decreae with increaing flow rate, a expected. H [] 35 Net Head 600rp rp 800rp 5 900rp 000rp Q [ 3 /] Figure 7. Net pup head Hydraulic efficiency rp rp 800rp rp 000rp Q/(ω*D 3 t ) Figure 8: Hydraulic efficiency

6 3 The hydraulic efficiency η h i hown in Fig. 8 a a function of the capacity coefficient, / ( ) Q ω at everal pup rotation peed. A can be oberved, the contant pup peed curve are all very cloe, confiring the validity of the iilarity rule derived fro dienional analyi. It i alo iportant to note that the hydraulic efficiency doe not vanih at hut off, ince the fluid keep being preurized. Figure 9 and 0 how the hydraulic head loe, h f, for each ipeller, a a function of the Reynold nuber at different pup peed. The Reynold in each ipeller channel wa defined by Re = ρ V n D h µ, where D h i the D h = 4 bc / b + C and average hydraulic diaeter between the inlet and outlet of each ipeller, defined a ( ) [ ( )] C = π r N δ, and V n i the average flow velocity relative to the ipeller. Both figure how that the head loe increae with increaing Reynold nuber, which ean that the loe increae with increaing flow rate. However, the contant peed curve are neatly apart fro each other for the econd ipeller, which alo preent higher loe in coparion with the firt ipeller. Thi can be due to the different nature of the flow arriving at each tage, and alo to the greater dicharge diaeter of the econd ipeller, which caue ore recirculation (i.e. flow eparation) in coparion with the firt ipeller. Note alo that the head lo doe not vanih at hut off, indicating the preence of other type of lo that do not depend of flow rate, uch a hock and recirculation. D t h f [] 4 3 h f - loe ( t ipeller) 000rp 900rp 800rp 700rp 600rp h f [] h f - loe ( nd ipeller) 000rp 900rp 800rp 700rp 600rp 0 0.E+00.E+04 4.E+04 Reynold nuber Figure 9: Head lot by fluid between inlet and outlet into the firt ipeller 0 0.E+00.E+04 4.E+04 6.E+04 8.E+04.E+05 Reynold nuber Figure 0: Head lot by fluid between inlet and outlet into the econd ipeller Figure for the firt ipeller and Fig. for the econd one how the dienionle head lo h / ( w / g) f a a function of the Reynold nuber for everal rotation peed. It can be oberved that, at a given rotation peed, the dienionle head lo decreae a the Reynold nuber increae, a for a pipe friction factor. Thi deontrate the adequacy of the Reynold nuber definition adopted, aking clear the effect of fluid vicoity and denity on the pup perforance. Alo, the dienionle head lo increae with the rotation peed, which preuably caue an increae in the turbulence and recirculation. Hence, a tentative odel for h f in a ingle ipeller can be uggeted: h f 3 e ωd Lchannel w ( w w ) ( w u co β ) = f channel Re,, k av k D Q + + (7) D g g g h ditribuited loe recirculation loe hock loe where the friction factor f and the paraeter k and k can be, in principle, deterined fro h f data. Note that at zero flow rate (hut-off) the two firt ter on the R.H.S. of Eq. (7) vanih, wherea the third one depend on the quare of rotation peed. Thi agree with the previou coent regarding Fig. 9 and 0. The low range of Reynold nuber data doe not allow for the oent to deterine if k and k depend on Reynold nuber and pup rotation or not. 5. Concluion Thi tudy preent a ethod to eauring hydraulic loe in centrifugal pup. The ethod i baed on the onedienional balance equation for a, linear oentu, angular oentu and energy.

7 Data collected in a two-tage pup working with water indicate that the hydraulic efficiency decreae with the flow capacity coefficient and the hydraulic loe increae with flow rate. When expreed in dienionle for, thee loe becoe equivalent to a friction factor, decreaing a the channel Reynold nuber increae. Thi ake clear the effect of fluid propertie (vicoity and denity) on the pup perfoance. A tentative odel for the evaluation of hydraulic loe i propoed, but ore data in the low Reynold nuber region i neceary for validation. h f /[w /(g)].e+0.e+0.e+00.e-0 Dienionle head lo ( t ipeller) 600rp 700rp 800rp 900rp 000rp h f /[w /(g)].e+03.e+0.e+0.e+00.e-0 Dienionle head lo ( nd ipeller) 600rp 700rp 800rp 900rp 000rp.E-0.E-0.E-03.E+0.E+03.E+04.E+05 Reynold nuber Figure : Dienionle head loe by fluid between inlet and outlet into the firt ipeller.e-03.e+0.e+03.e+04.e+05 Reynold nuber Figure :Dienionle head loe by fluid between inlet and outlet into the econd ipeller 6. Noenclature Sybol Decription Sybol Decription b blade width of ipeller, p preure, Pa r radial poition of a point on the ipeller, H net pup head, A cro ectional area of channel ( A = π r b), h theoretical head upplied to the fluid, z difference between inlet and outlet of ipeller, head lot by fluid between inlet and outlet of h f ipeller, ditance fro the ipeller entrance tip or the diffuer entrance tip to certain location on the W & break horepower ( ω T ), W trealine, τ w hear tre on the average ection, N/ W & echanical power lo ( ω T), W S w wetted perieter of fluid on the channel croection, η echanical efficiency T ipeller haft torque, N. β blade angle T ipeller friction torque, N. ρ denity fluid, kg/ 3 V abolute fluid velocity, / V t abolute tangential fluid velocity, / V n radial fluid velocity, / w fluid velocity relative to ipeller channel, / u peripheral velocity (ω.r), / Q flow rate, 3 / g acceleration of gravity, (9.8/ ) S w wetted perieter, ω angular velocity, radian/ Q L leakage flow rate η h hydraulic efficiency η V voluetric efficiency D h average hydraulic diaeter, C arc length, V n average radial velocity between the inlet and outlet of channel, / K lo coefficient due to inor loe L channel channel length, f curved friction factor to curved channel w o relative velocity in the bet efficiency point dienionle head loe (global friction dhl (BEP), / factor) D ipeller diaeter, Subcript Decription t firt nd econd entrance dicharge

8 Acknowledgeent The author thank ANP (Agencia Nacional do Petróleo), PETROBRAS and FINEP (Financiadora de Etudo e Projeto) for the financial upport in different part of thi work. Reference Aerican National Standard for Centrifugal Pup.Hydraulic Intitute, 994, Parippany. Church, A. H., 97, Centrifugal Pup and Blower, Robert E. Krieger Publihing Copany,USA, 308p. Gülich, J. F., 003, Effect of Reynold-nuber and urface roughne on the efficiency of centrifugal pup, ASME Journal of Fluid Engineering, 5, 4, pp Stepanoff, A. J., 957, Centrifugal and Axial Flow Pup, John Wiley & Son, nd Edition, USA, 46 p. Wen-Guang Li, Fa-Zhang Su, Cong Xiao, 00, Experiental Invetigation of Perforance of a Coercial Centrifugal Oil Pup, Tranaction of the ASME, 4, pp White, F. M., 994, Fluid Mechanic, McGraw-Hill. Reponibility notice The author are the only reponible for the printed aterial included in thi paper.