Theoretical background and the flow fields in downhole liquid-liquid hydrocyclone (LLHC)

Size: px

Start display at page:

Download "Theoretical background and the flow fields in downhole liquid-liquid hydrocyclone (LLHC)"

Cory Reed
5 years ago
Views:

1 AEC Web of Confeences 13, 3 (14) DO: 1.151/ maecconf/ C Owned by he auhos, published by EDP Sciences, 14 heoeical backgound and he flow fields in downhole liquid-liquid hydocyclone (LLHC) Haison Osei 1, a, Hussain H. Al-Kayiem and Fakhuldin Bin ohd Hashim 3 1,, 3 Depamen of echanical Engineeing, UP, 3175 onoh, Peak, alaysia Absac. Hydocyclone sysem fo downhole oil-wae sepaaion povides an effecive echnique of enhancing he economic viabiliy of highe wae-cu wells while a he same ime educing he isk of envionmenal polluion. his pape descibes he hydodynamics of he liquid-liquid hydocyclones and he flow fields wihin i ae paamoun fo achieving successful sepaaion pocess. Some of he impoan hydodynamic flow phenomenon wihin he liquid-liquid hydocyclone and how hey influence he sepaaion efficiency of wae/oil was analyed hough analyical soluion. he popeies of he liquids wee based on Bayan offshoe field measued popeies. he esuls indicaed ha hee ae wo swiling ones sepaaed by sagnan flow field. he inne is he ligh liquid one, while he oue is he heavy liquid one. 1 noducion he hydocyclone nowadays finds many applicaions in he sepaaion of solid liquid seams, liquid liquid seams and gas liquid seams [1]. hose ha ae used o sepaae suspended liquid doples fom anohe liquid seam ae emed LLHC. LLHC can be employed downhole fo he sepaaion of oil-wae poducs, due o is compacness, absence of moving pas and no chemical addiives. his echnology allows he poduced wae o be sepaaed downhole and e-injeced ino he same fomaion a suiable dephs. again educes he volume of poduced wae o he suface, wae eamen cos and possibiliy of polluion a he suface. he fluids wihin he cyclone undego some flow paens befoe achieving sepaaion. his pape pesens he mahemaical models ha can be used o pedic flow fields wihin LLHC and hei influence on he sepaaion pefomance of he sysem. Opeaional Pinciples of LLHC A schemaic dawing of a LLHC is shown in Fig. 1. is made up of a combinaion of conical and cylindical secions o pas. he uppe cylindical pa is closed a he op by a cove, hough which is he voex finde. Accoding o Bowe e al. [1], he fluid poduced when fed angenially ino he uppe cylindical poion of he LLHC ceaes a swiling movemen of he fluid making he heavie fluid facion, wae, o spin o he ouside of he LLHC wheeas he lighe fluid facion, oil, o migae owad he coe of he LLHC. Gome e al. [] poined ou ha, his swil movemen causes he flow paen wihin he hydocyclone o consis of a spial wihin anohe spial. he inne spial moves upwad wih he oue spial moving downwad. [] showed how he foced voex, exising in he aea close o he axis of he LLHC, and he fee-like voex, exising a he oue aea, behave and influence sepaaion wihin he LLHC. he oue voex moves downwads o he undeflow opening, wih he inne voex flowing in a evese diecion o he oveflow oule. he evese flow in he LLHC is due o he high swiling inensiy a he inle which inceases he cenifugal foce and causes he pessue o be high nea he wall egion and vey low owad he coe egion. Subjecing he undeflow oule o a highe pessue han ha of he oveflow, will cause he concenaed oil coe of his is an Open Access aicle disibued unde he ems of he Ceaive Commons Aibuion License., which pemis unesiced use, disibuion, and epoducion in any medium, povided he oiginal wok is popely cied. Aicle available a hp:// o hp://dx.doi.og/1.151/maecconf/14133

2 he voex o be foced o flow coune cuenly o he main flow[1, ]. he cenifugal foce developed acceleaes he seling ae of he fluid paicles heeby sepaaing hem accoding o sie, shape, and diffeence in densiy. Due o he acion of he dag foce, he oil moves o he coe egion of he LLHC and is caugh by he evese flow o be sepaaed hough he voex finde. he wae moves o he walls of he LLHC and migaes o he apex opening [, 3]. L L 1 L L 3 Di AEC Web of Confeences Do D α Dc β Du Geomeic lenghs (mm) D = 6; D i/d =.175; L 1/D = 1; D c/d =.5; D o/d =.5; L /D = 3; D u/d =.5; L/D = ; L 3/D = 15; α = o ; β = 1.5 o Figue 1: Schemaic diagam of LLHC (modified afe Colman & hew)[] n his wok, he mahemaical models ha descibe he hydodynamics of he LLHC and he flow paens ae pesened. hey wee coded in excel speadshee aking ino accoun he geomey of Fig. 1 and fluid popeies simila o Bayan oil fields - alaysia, o obain infomaion abou he hydodynamics and he flow fields likely o be obseved in he couse of using he LLHC. 3 Swil inensiy he swil inensiy, Ω, is poduced by he angenial inle of he LLHC and is defined as he aio of he ae of angenial momenum flux o he oal momenum flux a a specific axial locaion[4]. Howeve, eseaches have made some modificaions o he swil inensiy coelaion o help bee pedic i. Chang and Dhi coelaion [5] shown in Eq. 1 ook ino accoun only he momenum flux a boh he inle slo and he chaaceisic diamee posiion. o incopoae he fluid popeies and he inle configuaion, anilla [5] modified Chang and Dhi's model and ended up wih Eq.. Caldeney coelaion [6] shown in Eq. 3 included he semi angle, β, of he LLHC. By combining Caldeney and Edal coelaions, Gome [6] ended up wih Eq. 4 as he coelaion fo swil inensiy EXP.113 fo Dc Dc EXP fo e Dc Dc an.15 * EXP 1 1. an (3) e Dc (1) () 3-p.

3 CPE e an 1 EXP.15 * an (4) e Dc whee A c A (5) and is Fo Eq. and Eq. 4, n 1 exp and fo Eq. 3, 1exp n. U D c av e (6) c ρ c and µ c ae he densiy and viscosiy of he coninuous phase especively; is he axial posiion; Ac and A is ae he coss-secional aea a he chaaceisic diamee Dc and a he inle slo especively; U av is he aveage axial velociy a. Fo Eq. 3 and Eq. 4, n = 1.5 fo win inles and fo Eq., n = fo win inles. 4 Velociy Field wihin LLHC he velociy field in he hydocyclone has majo impac on he sepaaion of fluid. he swil inensiy is known o elae he local axial velociy o he angenial velociy. his means ha if he swil inensiy can be pediced fo a paicula axial posiion, he pedicion of he velociy pofiles wihin he cyclone becomes easie [3, 4]. 4.1 angenial Velociy he angenial velociy has been known and confimed expeimenally o be a combinaion of a foced voex and fee-like voex. he fome exiss nea he axis of he hydocyclone wih he lae exising nea he walls of he hydocyclone. Due o he angenial eny of he fluid ino he LLHC sysem, he fluid swils and poduces cenifugal foces which help sepaae he fluid paicles based on densiy diffeence wih he heavies o he lighes paicle aanged fom he cyclone s wall o is cene especively. hey poposed he following equaion fo he angenial velociy pofile [3, 4]: w m 1 exp B (7) U avc c c whee, U avc and c ae he is he aveage axial velociy and he adius a he chaaceisic diamee, Dc, especively; and is he adial posiion. m = Ω; B = 45.8Ω -.35 (win inles) 4. Axial Velociy he axial velociy pofile can be pediced by he use of a hid-ode polynomial equaion afe having imposed pope bounday condiions. he geneal fom is as follows [3]: 3 u a a a (8). 1 3 a4 whee a 1, a, a 3 and a 4 ae consans. he bounday condiions ae as follow: 1. du (he wall velociy consideed maximum); d. u ev (Velociy a he locaion of evese flow, ev, consideed eo); 3. du d (he velociy been symmeical abou he LLHC axis); 4. c u d U av c (Consevaion of mass). 3-p.3

4 f he bounday condiions ae subsiued ino Eq. 8, will yield he axial velociy pofile elaion [3]: u U av C 3 3 C.7 1 C ev ev C 3.7 (1) ev.3.1 (11) 4.3 adial Velociy he adial velociy, v, of he coninuous phase is vey small, and as a esul of ha many sudies choose o neglec i. can howeve be calculaed by using Eq. 1[3, 4]. v u an (1) AEC Web of Confeences 5 esuls and Discussion he compaison beween he vaious mahemaical models fo swil inensiy and how hey fi some seleced DOWS daa fom lieaue is shown in Fig.. Fom he figue, Chang and Dhi s model ove pedics he swil inensiy a /Dc<1 bu pedic he daa well a /Dc>. Gome and anilla models faily fi he daa wih Caldeney s model no fiing. he velociy pofiles pediced by he models wee compaed wih some field es daa fom DOWS opeaions. Fig. 3 shows he angenial velociy compaison of he vaious models wih field expeimenal daa. he y-axis epesens he cyclone axis wheeas he x-axis epesens he adial posiion. All he models show he ankine Voex shape, he combinaion of foced voex nea he LLHC axis and he fee voex nea he wall. Fom he figue, Gome model seems o give a good fi han he ohes. (9) Swil nensiy Chang & Dhi (1994) anilla (1998) Caldeney () Gome (1) Colman&hew Case daa Amini e al. Case 4 daa 1 3 /Dc Figue : Swil inensiy compaison angenial Velociy (mm/sec) /Dc =1.5 Chang & Dhi (1994) anilla (1998) Caldeney () Gome (1) Colman&hew case Amini e al. case 5 daa adius (mm) Figue 3: angenial velociy compaison he axial velociy pofile fo he flow wihin he LLHC is pesened in Fig. 4. he posiive values of he axial velociies coespond o downwad flow while he negaive values coespond o he evese flow. he model maches well he daa poins fo he downwad flow and no good in he evese flow egion. Howeve, in compuing he sepaaion efficiency of he LLHC, he evese flow velociy is no so impoan bu he adial posiion a which hee is eo velociy. his eason is well explained in Fig. 5. Fig. 5 pesens he pofile fo he adial posiions wihin he LLHC a vaious axial locaions whee he axial velociy is eo. he y-axis epesens he axis of he LLHC and he x-axis epesens he 3-p.4

5 adial posiion. By connecing all he adial posiions of eo velociy a he diffeen axial posiions wihin he LLHC give he pofile (plane) shown in Fig. 5. Fluids exising beween he wo pofile lines consiue he upwad spial and will be colleced as oveflow. hose fluids exising ouside he pofile lines will move downwads and be colleced as undeflow. hose exising on he pofile lines have fify-fify chance of going o eihe oule. Axial Velociy (mm/sec) /Dc = 1.5 Colman&hew Case daa Gome model adius (mm) Figue 4: Axial velociy compaison CPE -14 adius (mm) Figue 5: Pofile fo he adial posiions of eo axial velociy 6 Conclusion his wok has shown ha an in-deph knowledge of he hydodynamics and he flow paens wihin he LLHC ae vey impoan and should no be undeesimaed. he evese adius is an impoan faco in he sepaaion efficiency of he LLHC. Gome model agees wih mos of he expeimenal daa obained fom lieaue. An expeimen mus heefoe be pefomed using he poposed LLHC design modified afe Colman and hew and he daa ha will be obained used o validae he mahemaical coelaions poposed by he afoemenioned scholas. Acknowledgemen he auhos acknowledge Univesii eknolgi PEONAS fo he financial and echnical suppo o poduce his pape unde he eseach gan YUP FG 15-3AA-A73. efeences [1] B. E. Bowes,. F. Bownlee, and P. J. Schenkel, Developmen of a downhole oil/wae sepaaion and einjecion sysem fo offshoe applicaion. SPE Pod. & Faciliies, vol.15, no., pp , (). [] C. Gome, J. Caldeney, and S. Wang, L. Gome,. ohan, and O. Shoham, Oil/Wae Sepaaion in Liquid/Liquid Hydocyclones (LLHC): Pa 1 Expeimenal nvesigaion, SPE J., pp , (). [3] J. Caldeney, C. Gome, S. Wang, and L. Gome,. ohan, and O. Shoham, Oil/Wae Sepaaion in Liquid/Liquid Hydocyclones (LLHC): Pa echanisic odeling, SPE J., pp , (). [4] D.. Amini,. Golka and F. Esmaeiladeh, ahemaical modelling of a hydocyclone fo he down-hole oil wae sepaaion (DOWS) Chem. Eng. eseach and Design, vol. 9., pp , (1). [5]. S. anilla, Bubble ajecoy Analysis in Gas-Liquid Cylindical Cyclone Sepaaos, Sc. Disseaion, Dep. Peoleum Eng., Univesiy of ulsa, (1998). [6] C. H. Gome, Oil-Wae Sepaaion in Liquid-Liquid Hydocyclones (LLHC) Expeimen and odeling, Sc. Disseaion, Dep. Peoleum Eng., Univesiy of ulsa, (1). Axial Posiion (mm) 3-p.5

KINEMATICS OF RIGID BODIES

KINEMATICS OF RIGID BODIES KINEMTICS OF RIGID ODIES In igid body kinemaics, we use he elaionships govening he displacemen, velociy and acceleaion, bu mus also accoun fo he oaional moion of he body. Descipion of he moion of igid