Available online at Energy Procedia 4 (2011) Energy Procedia 00 (2010) GHGT-10

Transcription

1 Availabl oli at Ergy Procdia 4 ( Ergy Procdia 00 (010) Ergy Procdia GHGT-10 Exprimtal Studis of CO ad CH 4 Diffusio Cofficit i Bulk Oil ad Porous Mdia Datchawa Uatrakar a *, Koorosh Asghari a,b, Jos Codor a a Itratioal Prformac Assssmt Ctr for th Gologic Storag of Carbo Dioxid ( 10- Rsarch Driv, Rgia,SK., S4S7H9, Caada b Faculty of Egirig ad Applid Scic, Uivrsity of Rgia, 6 Rsarch Driv, Rgia, SK., S4S7J7, Caada Elsvir us oly: Rcivd dat hr; rvisd dat hr; accptd dat hr Abstract This papr prsts th rsults of xprimtal studis o diffusio cofficit of CO ad CH 4 i bulk oil ad porous mdia. A sris of tsts wr prformd ad diffusio cofficits wr stimatd from prssur profil as a fuctio of tim coupld with smi-aalytical solutio of th o-dimsioal diffusio quatio. Th prssur-tim profils wr masurd from xprimts. For ach ru, th gas diffusio cofficit was usd as adjustabl paramtr to fit th prssur-tim profil prdictd by smi-aalytical modl to th xprimtally masurd profil. Th diffusio cofficit rsultig from th bst-fit curv was cosidrd as th avrag diffusio cofficit. Thr mai coclusios wr obtaid from ths xprimts: (i) diffusio cofficits for both solvts, CO ad CH 4, icras liarly with tmpratur; (ii) diffusio cofficits of CO ar highr tha thos of CH 4, ad (iii) th ffctiv diffusio cofficits of CO i porous mdia hav lowr valus wh compard to bulk oil. Th importac of this study is likd to a bttr udrstadig of th molcular diffusio cofficit, which is sigificat i svral oil rcovry ad CO storag procsss sic it is oft cosidrd as th rat cotrollig mchaism. c Elsvir Publishd Ltd. byall Elsvir rights Ltd. rsrvd Op accss udr CC BY-NC-ND lics. Kywords: Diffusio Cofficit; Bulk Oil; Porous Mdia; EOR; Solvts 1. Itroductio Molcular diffusio is a sstial mchaism cotrollig th prformac of may solvt-basd procsss for oil rcovry. Ths mthods ivolv th ijctio of gasous solvts to dilut rsrvoir oil. Th rol of molcular diffusio is to hlp gas dissolv i th crud oil, rduc th ffct of viscous figrig, dclrat gas brakthrough, ad fially icras th oil productio rat (Zhag, Hydma & Maii 000). Th rat of mass trasfr causd by molcular diffusio is dtrmid by th diffusio cofficit, D, of gas ito crud oil, also calld gas diffusivity. I 1996, Mohammad Raizi dvlopd a prssur dcay tchiqu to stimat th diffusio cofficits of gass i liquids usig closd diffusio clls (Riazi 1996). I Raizi s tchiqu, th prssur-tim profil is obtaid as th gas phas diffusd ito th liquid phas ad th prssur of th systm chags. Oc th liquid phas is saturatd doi: /j.gypro

2 D. Uatrakar t al. / Ergy Procdia 4 ( Uatrakar, D.; Asghari, K; Codor, J. / Ergy Procdia 00 (010) with th gas phas, th diffusio cofficit ca b calculatd usig suitabl mathmatical modls. This xprimtal mthod was modifid by Y.P. Zhag (Zhag, Hydma & Maii 000). Th diffusio cofficit was usd as a adjustabl paramtr to obtai bst-fit curv of masurd prssur dcay data with th calculatd prssur dcay profil. Latr, Tharaivasa took ito accout thr diffrt boudary coditios (BCs): quilibrium, quasiquilibrium, ad o-quilibrium, by usig a tchiqu similar to that usd by Zhag (Tharaivasa, Yag & Gu 004) Th kowldg of th diffusivity of solvts ito havy oil i porous mdia is of grat sigificac i ptrolum girig. I porous mdia, fluids mov alog th tortuous path, which causs a logr ffctiv fluid flow path tha th appart lgth. Th molcular diffusio cofficit i porous rock is calld th ffctiv diffusio cofficit, D. May xprimtal studid hav also compard th valu of ffctiv diffusivity ad molcular diffusivity to obsrv th ifluc of th tortuosity of porous rock (Luo, Katzas 008, Afsahi, B. ad Katzas, A. 007, Salama, Katzas 005). Although th diffusio cofficits of gass i liquids hav b rportd by a umbr of rsarchrs, th accurat masurmt of both typs of diffusio cofficit udr th rsrvoir prssur is of grat importac bcaus of th rlativ lack of availabl data for th solvt-havy oil systms of itrst, spcially for th xprimts coductd i porous mdia. I this study, th diffusio cofficits of solvts i both bulk oil ad porous systms ar xamid by usig th history matchig tchiqu at tmpratur rag from 30 ºC to 55 ºC. Viscositis of two oil sampl ar 1,85 cp (Sampl# ad 8,154 cp (Sampl#). Accordig to th abov-mtiod thr BCs (Tharaivasa, Yag & Gu 004), th most appropriat itrfacial BCs for ach solvt-oil systm is foud by th miimum objctiv fuctio.. Exprimtal Masurmts.1. Diffusio cofficit masurmt for solvt-havy oil systms Exprimts wr carrid out at six diffrt tmpraturs: 30ºC, 35ºC, 40ºC, 45ºC, 50ºC, ad 55ºC for ach solvt-havy oil systm. Solvts usd for diffusivity masurmt i bulk oil ar CO ad CH 4. For th bulk oil stup, th followig assumptios wr tak ito accout: (i) gligibl ffct of oil swllig; (ii) o-volatil havy oil compots; (iii) costat gas diffusio cofficit. Solvt was ijctd ito diffusio clls filld with havy oil sampls. Ths diffusio clls wr placd i a air bath to maitai th tmpratur at th dsird tmpratur as show i Figur 1. Th iitial prssur was,665.5 kpa ad,415.3 kpa for CO -havy oil sampl#1 ad CO - havy oil sampl#, rspctivly. For masurig diffusivity of CH 4 i havy oil, th iitial prssur was 1,341.4 kpa for th CH 4 -havy oil sampl#1 ad 1,36. kpa for th CH 4 -havy oil sampl#. Th variatio of prssur for ach xprimt was rcordd as a fuctio of tim whil gas phas diffusd ito th liquid phas. A sigificat chag of prssur i th gas phas at th bgiig of th xprimt was obsrvd. It idicatd that th mass trasfr rat of gas is iitially high. Th xprimts wr cotiud util th gas phas prssur approachd a asymptotic valu, also kow as quilibrium prssur (P q ). Th diffusio cofficit of solvt gas ito havy oil is usd as a adjustabl paramtr to obtai bst match btw th xprimtal prssur data ad prssur-tim profil prdictd by th smi-aalytical modl... Effctiv diffusio cofficit masurmt for solvt-havy oil saturatd sad systms For th xprimts coductd i th prsc of porous mdia, th ffctiv diffusio cofficit of CO i havy oil sampl#1 saturatd-sad was masurd. Th opratig tmpraturs wr at 30 C, 35 C, 40 C, 45 C, 50 C ad 55 C. For calculatig ffctiv diffusio cofficit, four assumptios wr tak ito accout, (i) homogous porous sad, (ii) gligibl ffct of oil swllig, (iii) o-volatil havy oil compots, ad (iv) costat gas ffctiv diffusio cofficit. Coars sad was slctd to rprst th ucosolidatd porous mdia systm. Th aformtiod procdur for calculatig gas diffusivity ito bulk havy oil was also applid. Th diffusio cll was filld with th oil-sad mixtur ad solvt was ijctd ito th diffusio cll. Th iitial opratig prssur was,855 kpa. Th prssur-tim data wr masurd as solvt was dissolvd ito th oil phas util th prssur i th gas phas approachd a quilibrium prssur.

3 17 D. Uatrakar t al. / Ergy Procdia 4 ( Uatrakar, D.; Asghari, K.; Codor, J. / Ergy Procdia 00 (010) Tmpratur Cotrollr Prssur Gaug Fa Thrmocoupl Diffusio Cll P, T Solvt Elctric Hatr Havy Oil Fa Air Bath Figur 1 A block diagram of xprimtal st-up 3. Mathmatical Aalysis Th gral form of th o-dimsioal diffusio quatio is show i Equatio (, whr c( x, t) is th molar coctratio i havy oil, x is th distac from th bottom of th prssur cll to th itrfac, t is tim, ad D is th avrag diffusio cofficit of solvt i havy oil. c c = D ( t x Th mathmatical aalysis i this study is basd o th diffusio quatio, subjct to iitial boudary coditios at th bottom of th cll, ad thr itrfac mass trasfr modls (Zhag, Hydma & Maii 000). Th iitial gas coctratio i th oil phas is qual to zro throughout th cll sic thr ar o solvt molculs i th oil phas at th bgiig of th tst. Th mass trasfr flux at th bottom of th prssur cll is qual to zro at all tims bcaus of th rigid boudary at th bottom of th cll. With rspct to thr diffrt itrfacial BCs, th mathmatical aalysis for ach BC was dvlopd by Tharaivasa. I th quilibrium BC, th solvt-oil itrfac is assumd to b saturatd with th solvt at all tims. Th scod typ of BC is th quasi-quilibrium BC. I this cas, it is assumd that th solvt-oil itrfac is saturatd with th solvt udr th xistig prssur i th solvt phas. For o-quilibrium BC, th solvt-oil itrfac is assumd to b proportioal to th diffrc btw th solvt saturatio coctratio udr th quilibrium prssur ad th xistig solvt coctratio at th itrfac. I cojuctio with th quilibrium, quasi-quilibrium ad o-quilibrium boudary coditios, th aalytical solutio of Equatio ( ca b xprssd i dimsiolss form as show i Equatio () (4), rspctivly (Tharaivasa, Yag & Gu 004). C ( X, ) 1 ( ( + π cos X = () ( ) ( + π τ τ 4 = π Solvt Cylidr

4 D. Uatrakar t al. / Ergy Procdia 4 ( Uatrakar, D.; Asghari, K; Codor, J. / Ergy Procdia 00 (010) C ( X, ) = ( ( τ ( + π + π 4κ 1α τ τ ( + π cos X κ 1 4 = ( + ) 0 1 π κ1 4 + ( + 4κ β π κ 4 + τ ( + π τ 4 κ 4 1 ( + π ( + π τ 4 + (3) C ( X, τ ) = 1 = 1 si λ ( λ + si λ cosλ ) cos ( λ X ) λ τ (4) Th dimsiolss paramtrs, α, β, κ ad κ i Equatio (3) ca b stimatd from bst-fit curv aalysis. I 1, λ rprsts th Eig valus ad D k is th mass-trasfr Biot umbr. Th uppr ad lowr limits of th positiv root of th quatio (5) ar ( π ad ( π + π, rspctivly. k D ta λ = (5) quatio (4), ( =1,,3,... ) λ Th total mols of solvt dissolvd ito th oil phas, N diss (t), ar calculatd aftr th solvt coctratio i th oil phas is obtaid. As a cosquc, th mols of solvt rmaiig i th gas phas at ay giv tim, N rm (t) ar dtrmid by quatio (6), whr N i is iitial mols of solvt i gas phas. A quatio of stat for ral gas is applid to calculat th prssur i gas phas as dfid i Equatio (7). Th dtrmiatio of Z-factor i quatio (7) is calculatd by Zhou & Zhou (Zhou, Zhou 00. N rm ( t) = N N ( t) (6) i diss ( P T ) N ( t)rt Pcal ( t) Vsol = Z cal, rm (7) Oc a sris of prssur dcay curvs ar calculatd as a fuctio of tim, a mthod calld history matchig tchiqu is mployd to miimiz a objctiv fuctio whr th optimal valu of gas diffusivity is obtaid. Th objctiv fuctio ca b writt as: ΔP av = m i= 1 P cal ( t) Pxp ( t) m t = ti (8) 4 Rsults ad Discussio 4.1. Diffusio cofficit masurmt for solvt-havy oil systms Th diffusio cofficit for ach solvt-havy oil systm ca b obtaid as th objctiv fuctio is miimizd. Th diffusio cofficit of CO i oil sampl#1 is i th rag of to m /s. At a tmpratur of 30 C, th miimum objctiv fuctio dtrmid from th thr BCs ar rlativly th sam. Cosqutly, all thr BCs ar applicabl for th CO -havy oil sampl#1 systm at this opratig tmpratur. Howvr, th oquilibrium BC givs th bst matchig curv btw th masurd ad prdictd prssur-tim profil for th CO -havy oil sampl#1 systm at 35 C, 40 C, 45 C, 50 C ad 55 C. For th CO - havy oil sampl# systm, th diffusio cofficit falls i th rag of to m /s. At all opratig tmpraturs, th objctiv

5 174 D. Uatrakar t al. / Ergy Procdia 4 ( Uatrakar, D.; Asghari, K.; Codor, J. / Ergy Procdia 00 (010) fuctio is miimizd as th o-quilibrium BC is applid. Th dtrmid diffusio cofficits for both CO - havy oil systms ar plottd as a fuctio of tmpratur i Figur. It idicats that th CO diffusivity i oil sampl icrass liarly with icrasig tmpratur. This was xpctd sic diffusio is a viscosity dpdt mchaism ad oil viscosity rducs wh tmpratur icrass. Hc, it facilitats th mass trasfr for gas ito oil phas. Th diffusivitis of CH 4 i havy oil sampls ar show i Figur 3. Th rag of diffusio cofficit of CH 4 - havy oil sampl#1 systm is from to m /s, whras th diffusio cofficits of CH 4 i Sampl# ar i th rag of to m /s. For all gas-oil systms ad all opratig tmpraturs, o-quilibrium BC givs th bst match btw xprimtal ad prdictd prssur data. As xpctd, th icras i tmpratur iflucs th rductio i oil viscosity. Othr rsults wr obtaid wh comparig diffusio cofficits of CO ad CH 4 i both oil sampls, as show i Figur 4 ad 5. It ca b obsrvd that th diffusivitis of CO ar approximatly thrfold highr tha that of CH 4 i oil sampl#1, whil th diffusio cofficits ar twofold highr i oil sampl# wh CO was usd as solvt. Such a highr rat of diffusio may motivat oil compay to us CO basd hac oil rcovry (EOR) tchiqus mor tha thos usig CH 4 (i.., vapour xtractio, VAPEX, procss) 4.. Effctiv diffusio cofficit masurmt for solvt-havy oil saturatd-sad systms Th ffctiv diffusio cofficits of CO i oil sampl#1 i porous mdia is i th rag of to m /s, which is about thrfold lss tha its diffusivitis i bulk oil. Th miimum objctiv fuctio is obtaid wh th o-quilibrium BC is applid. Th compariso of th diffusio cofficit of gas i th sam oil sampl with ad without th prsc of sad is show i Figur 6. Th lowr molcular diffusio of gas i oil-saturatd sad is xplaid du to th tortuosity path i th porous mdia. I additio, similar to th diffusivity of gas i bulk oil, th icrasig tmpratur rsults i th icrasig diffusio cofficit, sic th viscosity of oil phas dcras as th tmpratur icras. Tabl 1 Diffusio cofficit for solvt-havy oil systms Oil Sampl Solvt gas P T D (MPa) (ºC) (10-8 m /s) Boudary coditio Ay BC at 30ºC Sampl#1 CO No-quilibrium BC (1,85cP) at ºC CH No-quilibrium BC Sampl# (8,154cP) CO No-quilibrium BC CH No-quilibrium BC Tabl Effctiv diffusio cofficit for solvt-havy oil saturatd sad systm P T D Oil Sampl Solvt gas (MPa) (ºC) (10-8 m Boudary coditio /s) Sampl#1 CO No-quilibrium BC (1,85cP)

6 D. Uatrakar t al. / Ergy Procdia 4 ( Uatrakar, D.; Asghari, K; Codor, J. / Ergy Procdia 00 (010) Figur Diffusivitis of CO i havy oil sampl#1 ad havy oil sampl# as a fuctio of tmpratur Figur 3 Diffusivitis of CH 4 i havy oil sampl#1 ad havy oil sampl# as a fuctio of tmpratur

7 176 D. Uatrakar t al. / Ergy Procdia 4 ( Uatrakar, D.; Asghari, K.; Codor, J. / Ergy Procdia 00 (010) Figur 4 Compariso of diffusivitis of CO ad CH 4 i havy oil sampl#1 as a fuctio of tmpratur Figur 5 Compariso of diffusivitis of CO ad CH 4 i havy oil sampl# as a fuctio of tmpratur

8 D. Uatrakar t al. / Ergy Procdia 4 ( Uatrakar, D.; Asghari, K; Codor, J. / Ergy Procdia 00 (010) Figur 6 Compariso btw diffusivitis of CO i bulk systm ad i porous systm 5. Coclusio I this study, th diffusio cofficits of CO ad CH 4 i havy oil wr dtrmid xprimtally. Th followig coclusios ca b draw from this study: - Th diffusivity of CO is highr tha that of CH 4 for a giv havy oil sampl ad opratig tmpratur - Th ffctiv diffusio cofficits of CO i porous mdia ar lss tha its diffusivitis i bulk oil bcaus of th tortuosity paths i th porous systm - I both bulk ad porous systms, icrasig tmpratur rsults i icrasig diffusio cofficit du to th rductio i oil viscosity 6. Rfrcs Afsahi, B. ad Katzas, A. 007, "Advacs i Diffusivity Masurmt of Solvts i Oil Sads", Joural of Caadia Ptrolum Tchology, vol. 46, o. 11, pp Luo, H. & Katzas, A. 008, "Ivstigatio of Diffusio Cofficits of Havy Oil ad Hydrocarbo Solvts Systms i Porous Mdia", SPE ,. Riazi, M.R. 1996, "A Nw Mthod for Exprimtal Masurmt of Diffusio Cofficits i Rsrvoir Fluids", Joural of Caadia Ptrolum Tchology, vol. 14, pp Salama, D. & Katzas, A. 005, "Moitorig of Diffusio of Havy Oils With Hydrocarbo Solvts i th Prsc of Sad", SPE/PS-CIM/CHOA 97855,. Tharaivasa, A.K., Yag, C. & Gu, Y. 004, "Compariso of Thr Diffrt Itrfac Mass Trasfr Modls Usd i Th Exprimtal Masurmt of Solvt Diffusivity i Havy Oil", Joural of Ptrolum Scic ad Egirig, vol. 44, pp Zhag, Y.P., Hydma, C.L. & Maii, B.B. 000, "Masurmt of Gas Diffusivity i Havy Oils", Joural of Ptrolum Scic ad Egirig, vol. 5, pp Zhou, L. & Zhou, Y. 001, "Dtrmiatio of Comprssibility Factor ad Fugacity Cofficit of Hydrog i Studis of Adsorptiv Storag", Itratioal Joural Hydrog Ergy, vol. 6, pp