Numerical Investigation of Nozzle Shape Effect on Shock Wave in Natural Gas Processing Abstract

Transcription

1 Numrical Invstigation of Nozzl Shap Effct on Shock Wav in Natural Gas rocssing Esam Jassim, hd Faculty of Enginring and pplid scinc rinc ohammd Univrsity, l-khobar Eastrn rovinc, Kingdom of Saudi rabia bstract Natural gas flow contains undsirabl solid particls, liquid condnsation, and/or oil droplts and rquirs rliabl rmoving quipmnt to prform filtration. Rcnt natural gas procssing applications ar dmandd compactnss and rliability of procss quipmnt. Sinc convntional mans ar sophisticatd in dsign, poor in fficincy, and continu lacking robust, a suprsonic nozzl has bn introducd as an altrnativ mans to mt such dmands. 3-D Convrgnt-Divrgnt Nozzl is simulatd using commrcial Cod for prssur ratio (NR) varis from. to. Six diffrnt shaps of nozzl ar numrically xamind to illustrat th position of shock-wav as such spot could b considrd as a bnchmark of particl sparation. Rctangl, triangl, circular, lliptical, pntagon, and hxagon nozzls ar simulatd using Flunt Cod with all hav sam cross-sctional ara. Th simpl on-dimnsional inviscid thory dos not dscrib th actual faturs of fluid flow prcisly as it ignors th impact of nozzl configuration on th flow proprtis. CFD Simulation rsults, howvr, show that nozzl gomtry influncs th flow structurs including location of shock wav. Th CFD analysis prdicts shock apparanc whn p 0 /p a >. for almost all gomtry and locats at th lowr ara ratio ( / t ). Simulation rsults showd that shock wav in Elliptical nozzl has th farthst distanc from th throat among th othrs at rlativly small NR. s NR incrass, hxagon would b th farthst. Th numrical rsult is compard with availabl xprimntal data and has shown good agrmnt in trms of shock location and flow structur.

2 Introduction In gas procssing industry, gas-xpansion quipmnt is mployd for obtaining low tmpraturs. s a rsult, natural gas flow could contain solid particls, liquid condnsation, and/or oil droplts. Existing such undsirabl phass in any natural gas piplin might caus svral problms in quipmnt and instrumntations. For instant, solid particls could dposit on th pip wall lading to partially blockag th flow. Th consquncs could b wors as th accumulation grows up rsulting in losing in flow prssur and rduction in transmission fficincy. articl layrs propagation tnd to gradually form a plug that sparats th pip into two prssur sctions: a high prssur sction btwn th high prssur gas sourc and th plug and a scond sction at low prssur btwn th plug and th gas rcovry division. In th upstram sction, a pip blast can occur du to prssur ris. Th plug can also bhav as a projctil that dstroys th pip whn th prssur diffrnc btwn th upstram and downstram sctions incrass. Th dposition of particls insid gas piplins is xtrmly undsird du to its nvironmntally and conomically dangrous impact. Th problms com up whn th solid matrial clogs th fluid stram, vn incrasing prssur drop and causing pip laks or xplosion. lso, a piplin blow-out ndangrs human lif as such accidnts hav rsultd in human daths in th past. In on incidnt, an xplosion causd a larg pic of pip to strik th forman, killing him []. Lysn [] listd thr incidnts in which projctils ruptd from piplins at lbows had causd loss of thr livs and ovr $7 million (US) in capital costs. nothr xampl is th ipr lpha disastr in th North Sa of July 6th, 988 which clarly dmonstratd th catastrophic consqunc of this typ of failur whr 65 of th 6 on board did. Furthr, th nrgy rlasd during this tragdy was stimatd to b qual to 0% of th UK nrgy consumption for that priod []. Th blockag incidnt du to dposition in natural gas piplin that occurrd on th Gas Export iplin (GE) of th attrhorn platform in 007 had rquird thr days for rsuming (Kan t al). During th rmdiation procss, about 400 bbl of condnsat and 5 scf of gas wr blown out. Statistical data showd that annually an oprating xpns gratr than $500 million is allocatd for particl dposition prvntion [3], almost half of which spnt for inhibitors [4]. Insulation of subsa Natural gas piplins costs up to $,000,000 pr mil to allviat scond phas formation [4]. lthough filtration procss capturs larg particls (mainly >5 µm), smallr siz particls will scap th procss and nd to b ffctivly rmovd. Bsids, th collision of th particls with th fibrs of filtration mdia rducs th kintic nrgy of th particls importd by th gas stram, vntuating adhring on th pip wall. Such problms, among many othrs, turnd rsarchr s attntions to invnt othr mthods of gas purification. Howvr, coming up with a robust dsign that hav capability to prform th task with minor problms is a challng. Sinc th common dsign challngs in all natural gas-xpansion applications ar th compactnss and rliability of procss quipmnt, suprsonic nozzls has bn introducd as an altrnativ dvic to mt such dmands.

3 Rcnt rsarch has introducd stat of art tchnologis basd on adiabatic cooling, th procss of gas xpansion in a suprsonic nozzl mployd for obtaining low tmpraturs. During th procss, part of gas nthalpy transforms to kintic nrgy on xpnss of tmpratur. Th gaind kintic nrgy can b rusd to incras th prssur in th systm of suprsonic and subsonic diffusrs. Th nozzl working sction liqufis targt componnts and significantly dcrass prssur and tmpratur at xit without utilizing xtrnal nrgy. Solid articls and condnsd droplts ar sparatd du to cntrifugal forcs that formd by swirling th gas ahad or at th outlt of th suprsonic nozzl. Th lattr mthod has bn usd by Twistr BV, Rijswijk, Nthrlands [5,6]. Installing a blad at th nd of th nozzl in th suprsonic flow zon immdiatly bfor th xtraction dvic provids swirling to th gas passing through it. Th Twistr sparator dhydrats gas and sparats havy hydrocarbons [7]. Th formr mthod, using a swirling dvic in th plnum chambr ahad of th nozzl, was indpndntly proposd by a group of Russian spcialists and dvlopd with thir participation by TransLang Tchnologis Ltd., Calgary. This mthod initiats gas swirling in th plnum chambr so that th tangntial vlocitis, whn combind with th cntrifugal forcs, sparat any scond phas particls formd in th suprsonic nozzl and dlivr thm to a spcial xtracting quipmnt. This approach minimizs total prssur losss in th shock wavs and sparats th flow dclration zon bhind th shock wav from th drop sparation zon [7]. Th compact dsign of suprsonic nozzls is a major advantag ovr traditional mans of natural gas trating tchnology. Comparison with othr convntional dvics such as Joul-Thompson valv and turboxpandr, has bn xprimntally studid. asurmnts showd that significant privilgs ar manifstd, in particular nrgy consumption and dvic compatibility. orovr, th high spd of th gas prvnts fouling or dposition of particls and th shock wav that would b gnratd will incras th vortx potntial of th flow, assisting in capturing smallr particls and rcovring th prssur of th flow [8]. Flow rgim in Laval Nozzl of diffrnt gomtry and sizs has bn numrously invstigatd xprimntally and computationally. Esam t al [9] hav xamind th impact of gomtry on th shock position numrically. Thy claimd that variation of divrgnt part of th nozzl would significantly chang th location of th shock wav. Th simplifying of complx flow in nozzl by assuming on-dimnsional flow rsults in significant rronous in prdicting flow structur. In rality, viscous ffcts, boundary layr/shock intraction, and flow sparation drastically altr th faturs of th flow. Commrcial softwar has bn mployd to invstigat th discrpancy of simpl ondimnsional thory with th numrical simulation outcom. Work of Khan t al [0] on th D convrgnt-divrgnt nozzl has shown that th location of shock prdictd by analytical thory drastically diffrs from computd simulation. Raman t al [] prsntd thir computational and xprimntal works on flow sparation ovr wid rang of NR. Thir rsults ar usd to furthr xamin th impact of th sparatd flow.

4 In trm of particl sparation potntial, Suprsonic nozzl has bn xprimntally xamind togthr with othr convntional dvics. Th outcom provd that at sam xtraction lvl, plants usd nozzl as a sparation dvic consum 0-0% lss comprssor powr than thos usd a Joul-Thomson valv or turboxpandr []. This may rturn to th fact that acclration gaind by th particl passs through th shock is hug and could b vn touch th ordr of 0 6 tims gravity acclration [9]. zad and Elgurri [] hav prsntd th impact of th nozzl gomtry on th flow physical bhavior along th CD nozzl. Two diffrnt lngths in th divrgnt portion wr mployd. Th analytical intrprtation of thir work has bn vrifid by flow visualization and prssur masurmnts. Thir xprimntal rsults concludd that th prformanc of th flow in CD nozzl could not b dscribd by simpl -D assumption as th flow bhavior is widly diffrd from thory prdiction. Th xprimntal masurmnts showd that xtnding th divrgnt part of nozzl rquirs highr NR to form shock. Similar conclusion was proposd by Esam t al [9], who conductd numrical study on -D CD nozzl with xtndd lngth. So far, thr is indispnsabl dmand to idntify optimal shap of suprsonic nozzl that is capabl to sparat particls mor fficintly. Th objctiv of th prsnt work is to lucidat th impact of nozzl shap on th location of shock wav and flow bhavior by mploying CFD Flunt cod. Rynolds-avrgd Navir- Stoks quation with k-ε quation turbulnc is usd to prdict shock position in symmtric 3-D nozzl. Th xprimntal rsults of apamoschou and Zill [3] ar utilizd as bnchmark for assssmnt. Thory and athmatical odling: Th aim of this sction is to brif th procdur of dtrmination th stramwis location of shock wav with knowldg of nozzl gomtry and NR. Consrvation of nrgy quation for -D invisid flow is writtn as: d udu 0 () ρ By ignoring th flow vlocity at nozzl ntranc, intgration of Eq. () lads to valuation of flow vlocity at any location along th nozzl: 0 u ( ) ρ () 0 0 Introducing ach numbr and rarrang for prssur ratio, Eq. () might tak th following form: 0 (3)

5 Th rlation btwn local ach numbr and th ara at that location is dfind by: ) ( * (4) whr * stands for th throat ara. Th product of Eqs.(3) and (4) would b: ) ( / 0 * (5) pplying of Eq.(5) on Nozzl xit: ) ( / * NR (6) Eq.(6) can b rwrittn in quadratic form for : [ ] ) ( * whr 0 NR C C (7) by solving th quadratic quation, knowing that ach numbr must b positiv, th flow xit ach numbr is dtrmind by: ( ) C (8) Eq.(8) rlats NR, divrgnt portion gomtry of th nozzl, and xit ach numbr. s mntiond arlir in this sction, th goal is to com up with a procdur that uss th right hand sid of Eq.(8) to valuat th shock location (/ * ). Such xprssions can b obtaind as follows: Th total prssur ratio across th shock ( 0 / 0 ) could b writtn as: NR (9) For isntropic flow, th inlt and xit total prssurs ar qual to th shock upstram and downstram total prssurs, rspctivly. By applying Eq.(3) at nozzl xit, Eq.(9) yilds to: NR 0 0 (0) Onc th total prssur ratio across th shock is dtrmind, th upstram ach numbr can b found by mploying th shock wav rlation, which taks th form:

6 0 0 Finally, th ara at which th shock occurs is dtrmind from Eq.(4): () ( ) () * Hnc, th procdur of dtrmination th shock location by knowing NR and xit to throat ara ratio can b summarizd as follows:. s NR and / * known, ach numbr at xit ( ) is valuatd using Eq.(8).. From outlt ach numbr and NR, total prssur ratio across th shock is dtrmind from Eq.(0). 3. Shock wav rlation, Eq.(), is mployd to find shock upstram ach numbr ( ). 4. Eq.() is usd for dtrmining shock wav ara. Th prsnc of th shock wav changs all flow conditions across it xcpt th stagnation tmpratur (or, mor prcisly, th stagnation nthalpy) sinc across th shock th flow is adiabatic. Th xtnt of th influnc of th shock on th flow conditions dpnds upon th ach numbr of th flow going into th shock. For thrmally and calorically prfct gass, th ratio of th static prssurs across th shock (p /p ) as a function of ach numbr ahad of th shock ( ) and th rlation btwn ach numbrs bfor and aftr shock wav ar rspctivly givn by: p ( ) (3) p [( ) / ] ( ) / (4) / Comparsion of thos rlations with th 3-D CFD rsults is conductd in this study to xamin th rang of rrounous that th -D assumption would b. Numrical Simulation Th finit volum solvr, FLUENT 6.3.6, is usd to obtain th numrical solution of th thrdimnsional comprssibl Navir Stoks (RNS) quations in connction with (k-ε) turbulnc modl quation. Th discrtizd quations, along with th initial condition and boundary conditions, wr solvd using th sgrgatd solution mthod, in which th consrvation of mass and momntum wr solvd squntially and a prssur corrction quation (SILE Schm) was usd to nsur th consrvation of momntum and th consrvation of mass (continuity quation).

7 Th govrning quations Th govrning quations consist of th continuity quation and th Rynolds-avragd govrning quations for stady comprssibl turbulnt flow coupld with th quation of stat, p qrt. Th systm of th govrning quations can b dscribd as follows: Turbulnc modl lthough svral turbulnc modls ar availabl, most of ths modls ar actually drivd from standard (k-ε) modl. Howvr thy ar vary in complxity and robustnss from two quation turbulnc modls to mor laboratd turbulnc modl. In th prsnt work, th standard (k-ε) modl is mployd to prdict th flow bhavior in th considrd physical domain. Eddy viscosity modls (EV) Th apparnt turbulnt sharing strsss might b rlatd to th rat of man strain through an apparnt scalar turbulnt or ddy viscosity. For th gnral Rynolds strss tnsor, th Boussinsq assumption givs: whr δ ij is th Kronckr dlta function (δ ij if i j and δ ij 0 if i j), k is th turbulnt kintic nrgy and µ t is th turbulnt viscosity. In ordr to obtain th turbulnt viscosity, othr transport quations ar ndd. Thss quations diffr from on modl to anothr. Th gnral transport quations for th adoptd modl ar givn blow, whil th diffrnt trms and cofficint of th turbulnc modls adoptd ar givn in Tabl.

8 Validation with xprimnt In ordr to validat th accuracy of th numrical simulation, comparison with th xprimntal data rportd by apamoschou and Zill [3] has bn conductd. Th gomtry illustratd in Figur () has th following dimnsions at xit: hight H.9 mm, width w 63.5 mm, and lngth L 7 mm from throat to xit.

9 Figur- schmatic of C-D Nozzl [3] Our comparison for shock formation as NR incrass is prsntd for / t.4. Th CFD analysis prdicts shock apparanc whn p 0 /p a >. and locats at th lowr ara ratio. Th locations of th shock wav for various NR prdictd by CFD simulation along with th xprimntal masurmnts prformd by [3] ar dpictd in Figur (). Th -D analytical formulas ar also mployd and plottd in th figur to dmonstrat th discrpancy of analytical approach with numrical and xprimntal outcoms. Th normalizd ara of th shock position w.r.t. throat ara (/ t ) is plottd against th NR. s illustratd in th figur, th prdiction of shock wav location using -D approximation is widly far from CFD rsult and xprimntal masurmnt, particularly at high NR. In rturn, 3-D numrical rsults ar shown to b in good agrmnt with th xprimntal data.

10 s / t.3.. ir / t.40 numrical apamoschou and Zill (004) on-dimnsional inviscid thory NR p /p 0 a Figur Shockwav location prdictd by CFD simulation vs. Exprimntal data prformd by Rf.[3] Contours of ach numbr at cntrlin plan ar plottd for diffrnt NR. s obsrvd in figur (3), for NR. th flow dos not rach sonic valu at throat. Hnc, th C-D nozzl bhavs as a subsonic flow. This significant conclusion controvrts th rsults of -D quations, which prdict shock xistnc at s / t.05. s th NR incrass, th shock manifsts nar th throat and movs firmly toward th xit of th divrgnt part of th nozzl. Figur 4 dpicts th impact of nozzl shap on shock location as a function of NR. lthough nozzl shap factor is not includd in th govrning quations that prsnt th gas motion in th suprsonic nozzl, CFD rsults confirm that a slight dviation in th shock location occurs whn th gomtry of th nozzl is changd.

11 (a) NR. (b) NR.4 Figur (3) Contours of ach numbr at Cntr lan

12 (c) NR.6 (d) NR.0 Figur (3) Contours of ach numbr at Cntr lan

13 s / t.. ir / t.40 Rctangl Circl Ellips Triangl ntagon Hxagon NR p /p 0 a.. Figur 4 Shockwav location prdictd by CFD simulation for diffrnt circular and noncircular shaps Conclusion: Sparation of undsirabl particls from natural gas flow using suprsonic nozzl is a promisd tchnology that turns oil and gas firm s attntion to nhanc th alrady xisting systms. Utilizing suprsonic nozzl for this purpos has showd a positiv impact on th sparation tchnology du to simplicity in dsigning, cost ffctiv in manufacturing, and fasibility in maintnanc. Th rsarch in this work focus mainly on mploying CFD commrcial softwar to study th influnc of nozzl shap on th shockwav location sinc such location impacts th turbulnc of th flow that vntually forcs small particls to mov toward th nozzl wall. Hnc, improvs th collction fficincy. Th numrical rsults show that nozzl shap is slightly changd with th shap of th nozzl. Elliptical Nozzl prdicts shockwav a bit latr than othr shaps for spcific NR. Howvr at high NR hxagon nozzl is th on among th rst whos shock location bcoms th farthst from th nozzl throat.

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