Liquid Holdup Correlation for Inclined Two-Phase Stratified Flow in Pipes

Transcription

1 Kufa Joural of eer, Vol., No., 009 qud Holdup Correlato for Icled Two-Phae Stratfed Flow Ppe hmed Sab Naj btract: I th tudy, et of explct equato to predct the lqud holdup cled tratfed, two-phae, a-lqud flow ha bee developed. Th tudy mlar to bdul Majeed' tudy for predct the lqud holdup horzotal ppe. The expermetal tet coducted from everal ource publhed the lterature ad other upublhed elected from the Iraq-Ol well. The comparo acheved u the FPR fucto veru may of prevou tude. The comparo reveal that the preet correlato em-detfcato wth the oral correlato by Tatel-Dukler model ad t dplay that the ueted correlato ha the bet performace tha the other. :. -.. ( ). ( - ). Itroducto: There are may tude had bee acheved to predct the lqud holdup ppe. Some of them, tuded the tratfed flow horzotal ppe whle the other tuded the flow cled ppe. Moreover, mot of them were emprcal tude ad developed model already vald for ther expermetal data oly. Tatel-Dukler (976) tuded the tratfed flow ad they derved a et of equato to predct the lqud holdup. Ther tudy wa deped o the mplct oluto of two-phae mometum equato. Uually, th oluto adopt the terato method to locate the depedet term ( h ). The fal tep of ther tudy wa draw a compact plot of the depedet term ( h ) veru ockhart-martell parameter (X). The plot cot of mult-curve; each oe pecalzed to the clato term (Y). Ther procedure tll ued to th tme. Barea (987) ued th procedure to develop ther ufed model to predct the flow patter two-phae, ar-water flow for the whole clato ale. Xao et al. (990) alo ued Tatel-Dukler procedure to develop ther mechatc model to predct the flow patter, lqud holdup ad preure drop horzotal ppele. bdul Majeed (996) uet ew procedure to mplfy ad to modfy the model of Tatel-Dukler by covert t to two explct equato to predct the lqud holdup. Thee equato are expreed the depedet term ( h ) ad the ockhart-martell parameter a depedet term ad for horzotal flow oly. There are may vetator adopted the model of Tatel-Dukler a Gokcal et al (006), tuded the effect of the vcoty o the flow patter, lqud holdup ad preure drop deped of the model of Tatel-Dukler. atly, drto et al (008) tuded the tratfed two-phae flow by u the model of Tatel-Dukler.

2 Kufa Joural of eer, Vol., No., 009 I the preet tudy, the procedure of bdul Majeed wll exteded to cover the upwardly cled flow ad et of equato wll ueted to predct the lqud holdup cled ppe. xpermetal Data: There are o expermetal tet developed the preet tudy, the ued expermetal data coducted by ome tude publhed the lterature ad other coducted from the Iraq-Ol well, thee data ha bee examed by u the flow patter map of Mukherjee-Brll (985) [] to prove the ext of the tratfed flow. Thee ource of data dplayed table () ad table (). Table (): The Data Source R Referece No. of Data Iclato le Dameter (m) Sytem Flud bdul Majeed 0 0 o r-keroee Mukherjee ad Brll 0 o r-keroee 3 Iraq-ol well 7 0 o Natural acrude ol 4 Smth 99 o r-ol Table () dplay the rae of the tet udertak the preet work. Table (): Flow Codto Rae R The Property Mmum Maxmum Superfcal a velocty m/ec Superfcal lqud velocty m/ec verae Preure KPa verae Temperature o C qud Holdup dmeole The properte of each phae could be predcted by the faclte ytem ad a follow [ ad 0]: T K av P [ 87 (73 o av 83. k/m 3 T av 0.00XP ( T ) K av T T av av o 6.6 mpa. )]

3 Kufa Joural of eer, Vol., No., 009 The ubcrpt; K: keroee : r o: Ol Naj ad l-kayem (00) [] dplayed et of equato to etmate the flow properte of atural a ad lve crude ol for Iraq ol well. Tatel-Dukler (976) Model: Tatel ad Dukler (976) derved the two-phae, tratfed, a-lqud mometum equato a: V f X V d V V d 4 Y 0 f () The upercrpt ( ) over ay varable equato () repreet t dmeole form. ockhart-martell parameter (X) ad the clato parameter (Y) are defed a: m V V X V V m d V d Y C V ad ( ) the clato ale. For turbulet flow, t ue m0. ad C0.046 whle ue m ad C6 for lamar flow. (f ) ad (f ) are repreet the terfacal ad a-wall frcto factor repectvely. Now, all varable equato () are poble to be etmated by u fure () deped o the dmeole lqud level heht ( h ). S d Ga V h S qud V S Fure (): The Cofurato of tratfed flow patter 3

4 Kufa Joural of eer, Vol., No., the follow: d h h h co 0.5 ) ( h ) (h / V 0.5 / V / 4 d / 4 d Xao et al (990) developed equato to etmate the lqud holdup tratfed flow, th equato fucto of ( h ) alo: H () Where: the wet ale by the lqud ad t calculated by: h co Tatel ad Dukler (976) propoed that the rato f / f uty, hece they could predct the lqud holdup by the follow procedure:. Solve the equato () teratvely for ( h ).. tmate the lqud holdup by u the equato (). bdul Majeed (996) Model: bdul-majeed tuded the horzotal flow, th tate the value of (Y) wll be zero ad equato () reduced to: 0 d V f f V V d V X (3) Sce ( h ) rouded betwee zero ad uty, he ueted that the equato (3) could be olved for (X), ad by u the equato () he correlated (H ) a a fucto to (X). He ueted two equato: oe for turbulet flow whle the other wa for lamar flow a the follow:. For Turbulet Flow: H XP( R R R 4 ). For amar Flow: H XP( R R R R 4 ) Where; R (X)

5 Kufa Joural of eer, Vol., No., 009 Preet Correlato: Curretly, equato () could be olved for (X) related to the chae of ( h ) from zero to uty for each matude of (Y) ad H could be calculate by u equato (), a curve ftt acheved for H a fucto to the parameter (X), th proce led to the follow equato: H 0 Z (4) Where: Z N a b 0 N: No of coeffcet (a ) a : Coeffcet et from table (3) or table (4) accord to the flow type (turbulet or lamar). b o ( X) 0 The follow procedure wll be ueted:. Calculate (Y) accord to clato ale.. Calculate the value of ockhart Martell Parameter (X). 3. For turbulet flow: ccord to the value of (Y), ue table (3) to locate the coeffcet of (a). 4. For lamar flow: ccord to the value of (Y), ue table (4) to locate the coeffcet of (a). 5. The lear terpolato wll be ueted for o-avalable value of (Y). 4. Ue equato (4) to predct the lqud holdup (H ). Work Procedure: I the preet work, two tep have bee acheved: - Developmet of the model: bdul-majeed (996) preet a procedure to predct the lqud holdup for horzotal flow u equato () ad (3) ad he ueted u h model tead of Tatel-Dukler model. Th procedure adopted the curret work to develop the preet model to predct the lqud holdup for cled flow clud the horzotal flow. - Tet the model: The preet model ha bee teted relate to the model of Tatel-Dukler, the tet clude the follow tep:. ume varou matude for (X) ad (Y).. Ue the preet model to predct the lqud holdup. 3. Ue Tatel-Dukler to predct the lqud holdup. Now, the value of (H ) by the preet model ad thoe predcted by the Tatel-Dukler model plotted aat (X) a how fure (), ad the value of the averae error betwee the predcto of them dplayed table (5) for elected value of (Y), thee value had bee dplayed the reult of Tatel-Dukler (976) work. The other value of (Y) are curretly udertak to cover a wde rae of the clato effect. 5

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8 Kufa Joural of eer, Vol., No., 009 *** Tatel-Dukler Model The Preet Model Y 0 Y qudholdup ockhart-martell Parameter (X) Fure (): Comparo betwee the Preet work ad Tatel-Dukler Model for dfferet Value of (X) ad (Y) Table (5): The error betwee the preet work ad the oral model of Tatel-Dukler for dfferet value of (Y) Matude of (Y) verae rror The fure () ad table (5) how the cocdece tate of thee model; therefore; t ueted to ue the preet model tead of the model of Tatel- Dukler the predcto the horzotal ad cled flow. The ctvty of the Preet Model: The preet model ha bee teted u everal model, ome of them ued the predcto horzotal flow a bdul Majeed (996) ad other ued for cled ppe a Gozhov et al. (967), Mukherjee-Brll (985) ad Be-Brll (986). The tet acheved u the expermetal data how table () ad table () by u the relatve performace factor (F PR ) whch defed a: F PR max m m max m m 3 3max 3m 3m 8

9 Kufa Joural of eer, Vol., No., max 4m 4m 5 5max 5m 5m 6 6max 6m 6m (5) It oberved that the relatve performace factor deped o may parameter defed the follow equato:. verae rror: (6). bolute verae rror: (7) (8) Stadard Devato: ( ) 4. verae Percet of rror: 4 P (9) 5. bolute verae Percet of rror: 5 P (0) () 6 6. Percet Stadard Devato: ( P ) Where the error () ad the percet error (P) are defed a: H H ad P 00 % cal mea H mea The rae of th factor lmted betwee zero ad 6. The zero value dcate the bet performace [ar et al. (994), bdul-majeed (997 ad 000) ad Naj,. Sab ad l-kayem, H. H. (00)]. The Reult ad Dcuo: The tattcal reult of the preet model ad the other model ha bee dplayed accord to the clato ale: Horzotal Flow Data: The reult were dplayed raphcally fure (3) throuh fure (6) ad tabular form a table (6). The raph how the bet pread of the predcted holdup related to the expermetal holdup tha the other whle the behavor of the bdul- Majeed wa the ecod bet. It oberved that the preet model ha a uperor reult tha the other model where t ha (F PR 0) a how table (6). 9

10 Kufa Joural of eer, Vol., No., H cal H mea Fure (3): The calculated lqud holdup by the preet model for horzotal flow data H cal H mea Fure (4): The calculated lqud holdup by bdul-majeed model for horzotal flow data H cal H mea Fure (5): The calculated lqud holdup by Be-Brll model for horzotal flow data. 0

11 Kufa Joural of eer, Vol., No., H cal H mea Fure (6): The calculated lqud holdup by Mukherjee-Brll model for horzotal flow data. Table (6): The Stattcal Reult U Horzotal Data The Method SD 0-5 P P SDP F PR Preet Model bdul- Majeed Be-Brll Mukherjee- Brl Icled Flow Data: The reult of the whole model have bee dplayed raphcally fure (7) throuh fure (0) ad the tattc how table (7). The reult how that the preet model the bet the predcto of the lqud holdup tha the other. It oberved alo, the bad reult of the model by Mukherjee -Brll (985) ad Be - Brll (986) pte of thee method are pecfed for the cled flow. Fally, the model of Gozhov et al. (967) ha ood reult a how table (7)

12 Kufa Joural of eer, Vol., No., Hcal H mea Fure (7): The calculated lqud holdup by the Preet model for Icled flow data Hcal H mea Fure (8): The calculated lqud holdup by Be-Brll model for Icled flow data Hcal H mea Fure (9): The calculated lqud holdup by Mukherjee-Brll model for Icled flow data.

13 Kufa Joural of eer, Vol., No., Hcal H mea Fure (0): The calculated lqud holdup by Gozhov et al model for Icled flow data. The Method Preet Model Table (7): The Stattcal Reult U Icled Data Oly SD 0-5 P P SDP F PR Be-Brll Mukherjee- Brll Guzhov et al Cocluo: The ued correlato of Mukherjee-Brll (985), Be-Brll (986) ad Guzhov et al (967) are developed by reardle the lqud level cocept, therefore, they ave the bad reult, t foud that th factor locate the ecoutered flow patter [7]. Th cocept adopted by the mechatc model of Tatel-Dukler. The procedure of etmato the lqud holdup the lat model eed to a teratve techque. The preet work coverted th lethy techque to mple equato clud the clato mpact. Therefore, The model of Tatel-Dukler ad the preet correlato ave coveret reult a how table (5), ad ave bet performace compar wth the other method, a dplayed table (6) ad fure (3) to (6) for horzotal flow, ad a how table (7), the fure (7) to (0) for cled flow. From the whole table ad fure, the follow cocluo may be reveal:. The reult of the preet correlato ad the model of Tatel-Dukler are very coveret, therefore, t recommeded to ue the preet method tead of the model of Tatel-Dukler. 3

14 Kufa Joural of eer, Vol., No., 009. The reult of the preet method the bet performace the other ued model for both horzotal ad cled flow due to t adopt the effect of the clato. 3. The matude of the lqud holdup horzotal flow larer thoe cled flow becaue of the clato effect. ckowledemet: The uthor rateful ad thakful to Prof. Dr. G. H. bdul-majeed at Computer cetre, Bahdad Uverty, Iraq, for h ueto about th work. Nomeclature: cro ectoal area (m ) D ppe dameter (m) f frcto factor (dmeole) F PR relatve performace factor (dmeole) H qud Holdup (dmeole) h qud level heht (dmeole) P av averae preure (N/m ) Q lqud dchare (m 3 /) Re Reyold umber (dmeole) phae permeter (m) V velocty (m/) X ockhart-martell Parameter (dmeole) Greek ymbol: Relatve rouhe (dmeole) Shear tre (N/m ) Dety (k/m 3 ) Vcoty (N /m ) le of clato (de.) Subcrpt: w wall-a w wall-lqud a lqud terfacal uperfcal a uperfcal lqud t tralato Supercrpt: Dmeole * crtcal value Referece: bdul-majeed, G. H. (996): qud Holdup Horzotal Two-Phae Ga- qud Flow, Joural of Petroleum Scece ad eer 5, PP B. Gokcal, Q. Wa, H.-Q. Zha ad C. Sarca (006): "ffect of Hh Ol Vcoty o Ol/Ga Flow Behavor Horzotal Ppe", the U. of Tula SP ual Techcal Coferece ad xhbto held Sa too, Texa, U.S.. 4

15 Kufa Joural of eer, Vol., No., 009 dru, P. ad Pere,. N.: (987) Stratfed Ga-qud Flow Dowwardly Icled Ppe, I. J. Multphae Flow 3, No. 4, Baker,., Nele, K. ad Gabb,.: (988) Preure o qud Holdup Calculato Developed, Ol ad Ga J, Brll, J. P. ad Be, H. D.: (986) Study of Two-Phae Flow Ppe, ffth dto, The Uverty of Tula, U. S.. Cheremoff, N.P., ad Dav,. J.:(979). Stratfed Turbulet-Turbulet Ga- qud Flow, ICh. J.5, No., Hamerma, P. J. ad Hart, J.: (987) Preure Drop Correlato for Ga/qud Ppe Flow wth a Small qud Holdup, Chem.. Sc.4, No. 5, Mukherjee, H.: (985) xpermetal Study of Icled Two-Phae Flow, Ph. D. Dertato, the Uverty of Tula. N, drto, C. Tzotz ad T.J. Haratty (008): "INTRFCI SHR STRSS IN WVY STRTIFID GS-IQUID TWO-PHS FOW", 5th uropea Thermal-Scece Coferece, the Netherlad. Naj,. Sab ad l-kayem, H. H. (00): Study of Two-Phae Flow Horzotal ad Icled Ppe, M. Sc. Dertato, Mech.. Dept., Collee of eer, l-mutaryah Uverty. Shoham, O. ad Tatel, Y.: (985) Stratfed Turbulet-Turbulet Ga-qud Flow Horzotal ad Icled Ppe, ICh J.30, No.3, Smth, T. N. ad Tatel, R. W.: (966) Iterfacal Shear Stre ad Mometum Trafer Horzotal Ga-qud Flow, Chem.. Sc.., Steve P. Smth, (999)" xpermetal Ivetato of multple oluto for lqud holdup upward cled tratfed flow, M. Sc. The, Uverty of Calary, Caada. Tatel, Y. ad Barea, D.: (990) Cotet pproach for Calculat Preure Drop Icled Slu Flow, Chem.. Sc. 45, No. 5, Tatel, Y. ad Dukler,..: (976) Model for Predct Flow Reme Trato Horzotal ad Near Horzotal Ga-qud Flow, ICh J., No., Wall, G. B.(969): Oe Dmeoal Two-Phae Flow, McGraw Hll. Xao, J. J., Shoham, O. ad Brll, J. P.: (990) compreheve Mechatc Model for Two-Phae Flow Ppe, 65 th. Tech. Cof., Soc. Pet.., New Orlea,, Pap. SP 063, PP. 4. 5