SPE Paper Number 93879

Transcription

1 SPE Papr Numbr Monioring Warflood Opraions: Hall s Mhod Rvisid D. B. Silin, SPE, Lawrnc Brkly Naional Laboraory and Univrsiy of California, Brkly; R. Holzman, Univrsiy of California, Brkly; T. W. Pazk, SPE, Univrsiy of California, Brkly; J. L. Brink, SPE, ChvronTxaco Producion Company Copyrigh 5, Sociy of Prolum Enginrs Inc. This papr was prpard for prsnaion a h 5 SPE Wsrn Rgional Ming hld in Irvin, CA, U.S.A., 3 March 1 April 5. This papr was slcd for prsnaion by an SPE Program Commi following rviw of informaion conaind in a proposal submid by h auhor(s). Conns of h papr, as prsnd, hav no bn rviwd by h Sociy of Prolum Enginrs and ar subjc o corrcion by h auhor(s). Th marial, as prsnd, dos no ncssarily rflc any posiion of h Sociy of Prolum Enginrs, is officrs, or mmbrs. Paprs prsnd a SPE mings ar subjc o publicaion rviw by Ediorial Commis of h Sociy of Prolum Enginrs. Elcronic rproducion, disribuion, or sorag of any par of his papr for commrcial purposs wihou h wrin consn of h Sociy of Prolum Enginrs is prohibid. Prmission o rproduc in prin is rsricd o a proposal of no mor han 3 words; illusraions may no b copid. Th proposal mus conain conspicuous acknowldgmn of whr and by whom h papr was prsnd. Wri Librarian, SPE, P.O. Box , Richardson, TX , U.S.A., fax Absrac Hall s mhod is a simpl ool usd o valua prformanc of war injcion wlls. I is basd on h assumpion of sadysa radial flow. Bsids hisorical injcion prssurs and ras, Hall s mhod rquirs informaion abou h man ambin rsrvoir prssur, p. In addiion, i is assumd ha h quivaln radius, r, of h rsrvoir domain influncd by h wll is consan during h obsrvaion priod. Nihr p nor r ar availabl from dirc masurmn. Hr w modify and xnd Hall s plo analysis, calling i slop analysis. Our modificaion rlis on h analysis of h variaions of slop of h cumulaiv injcion prssur vrsus cumulaiv injcion volum. In paricular, our slop analysis producs an sima of h man ambin rsrvoir prssur, and rquirs only h injcion prssurs and ras. Such daa ar rouinly collcd in h cours of a warflood. No ha h slop analysis mhod rquirs no inrrupions of rgular fild opraions. Th proposd slop analysis mhod has bn vrifid wih h numrically gnrad prssur and ra daa, and sd in h fild. In boh cass i provd o b accura, fficin, and simpl. Th obaind ambin rsrvoir prssur sima can b usd o corrc h Hall plo analysis or o map h avrag rsrvoir prssur ovr svral parns or an nir warflood projc. Such maps can hn b usd o dvlop an fficin warflood policy, which will hlp o arrs subsidnc and improv oil rcovry. Inroducion Monioring and conrol of prformanc of ach individual wll is an imporan componn of succssful oil rcovry opraions. Th dramaic progrss in informaion chnology ovr h pas dcad has mad i possibl o collc and sor hug volums of high-qualiy producion and injcion daa. Ths daa, if approprialy inrprd, provid nw insighs ino rsrvoir dynamics across mulipl mporal and spaial scals. Thrfor, fficin procssing and inrpraion of h high-frquncy fild masurmns is a ask of crucial imporanc o modrn managmn of oil&gas rcovry projcs. This papr dals wih problms rlad o monioring and conrol of warflood opraions. Th ncssiy of collcing and procssing numrous masurmns was undrsood dcads ago 1. Rcnly, ChvronTxaco wih paricipaion of h Lawrnc Brkly Naional Laboraory and h Univrsiy of California, Brkly, dvlopd a concp of fild-wid survillanc and conrol of warflood. This concp is bing implmnd in h Los Hills oil fild. Th work rpord hr is a par of his ffor. Warflood prformanc in an nir oilfild rsuls from h qualiy of ach individual wll. Th global projc objcivs ar drivd from a fild-scal analysis, such as inspcion of salli imags for surfac subsidnc and uplif, and calculaion of h fluid injcion-wihdrawal balanc. 3 Bu h subsurfac rsrvoir can only b accssd and conrolld hrough wlls. Thrfor, i is criically imporan o hav fficin mhods for adqua assssmn and monioring of wll prformanc, and for rgular valuaion of rsrvoir condiions nar h wllbor. Tradiional ransin wll ss hav bn usd o valua h avrag nar-wllbor formaion ransmissiviy 4. Such ss inrrup rgular fild opraions. Thir inrpraion is basd on analysis of ransin ffcs aking plac a im scals which ar shor rlaiv o hos of fluid injcion and producion. On on hand, unlss hr is a pip-lik circulaion of injcd fluid bwn an injcor and h surrounding producrs, h injcion rsuls in vr-changing rsrvoir condiions. On h ohr hand, hs changs may b almos imprcpibl ovr a ypical obsrvaion im inrval. Thrfor, normal rsrvoir procsss can b calld quasi sady-sa. In ral lif opraions, shor-im flucuaions of h injcion prssurs and ras a h wll ar inviabl. Sparaion of hs shor-im ransin ffcs and long-im quasi sady-sa procsss is on of h mos imporan asks of wll prformanc monioring and diagnosics, 5-7 crucial o h informaion-drivn oilfilds of h fuur (h IFilds). Hall s mhod 8, s also 4, is an alrnaiv o ransin wll s approach. Tchnically, i is vry simpl: jus plo h im ingral of injcion prssur vrsus cumulaiv injcion. Th

2 SPE ingraion auomaically filrs ou shor-im flucuaions. Th slop of Hall s plo is inrprd as an indicaor of h avrag wll injciviy. As inpus, Hall s mhod only rquirs rgular collcion of injcion ras and injcion prssurs, ha ar a par of rouin warflood opraions. A normal condiions, h plo is a sraigh lin and kinks on h plo should indica changs of injcion condiions. This mhod has bn usd xnsivly o assss succss of a wll ramn by comparing h slops bfor and afr h ramn 9, 1. Howvr, h simpliciy of Hall s mhod can b dciving. Rigorously spaking, a corrc Hall plo inrpraion rquirs informaion abou h rsrvoir prssur a h disanc qual o h man influnc radius of h wll. If Hall s mhod is applid wihou a priori knowldg of h ffciv ambin rsrvoir prssur, hn h conclusion ha a kink in h plo is an indicaion of changs in h wll injciviy can b wrong. Esimaion of h rsrvoir ransmissiviy from h Hall plo is impossibl, unlss h influnc radius is known and dos no chang during obsrvaions. Nihr h rsrvoir prssur a h boundary of h influnc domain nor h influnc domain siz is availabl from masurmns. Thr is no vidnc ha h influnc radius dos no chang afr a wll ramn or wih changing injcion ra. On h conrary, i is fair o assum ha h variabl wll-opraion condiions affc ha radius. Thrfor, his papr rvisis h Hall plo mhod and inspcs is horical background. Applicaion of Hall s analysis naurally xnds o non-radial flow mod, bu h quasi-sady-sa flow assumpion canno b rlaxd. In raliy, h sady-sa flow is inviably disurbd by shorim (high-frquncy) flucuaions of prssurs and ras. I urns ou ha analysis of h Hall plo slop flucuaions, which w call slop analysis, rvals vry imporan informaion abou h ffciv rsrvoir prssur nar h wllbor and h injciviy of h wll. Lik Hall s mhod, h slop analysis is vry simpl. As inpus, i only rquirs injcion ra injcion prssur daa. Informaion abou h rsrvoir prssur is no rquird, bu is drivd insad as a par of h analysis. Th dns wll spacing in h Los Hills oil fild maks i possibl o cra maps of his ffciv rsrvoir prssur on diffrn im inrvals and o monior h rsrvoir dynamics a h fild scal. Comparison of hs maps wih salli subsidnc imags provids valuabl clus as how o mak warflood mor fficin and o avoid unncssary wll failurs. Jim, plas look if you can labora hr and hr Th papr is organizd as follows. Firs, w rviw h horical background of h Hall plo mhod. This par is includd o mak h prsnaion slf-conaind. Scond, w dmonsra ha Hall s mhod can lad o wrong conclusions if h rsrvoir prssur and h raio bwn h influnc radius and h ffciv wllbor radius ar unknown. W do so by analyzing simulad daa producd by a forward modl of war injcion. W us h mhods 11,1 dvlopd for wll-s analysis, whil accouning for rgular fild opraions. Third, w propos a nw wll diagnosics mhod, calld slop analysis. W illusra his mhod using simulad daa. In h concluding par, w vrify our analysis agains ral injcion daa from h Los Hills oil fild. Hall Plo: Thorical Background Hall plo is a ool o analyz sady-sa flow a an injcion wll. Originally, i was basd on h radial flow modl 13. According o his modl, μ r p = p + ln Q.(1) w π kh rw whr p w and p ar h downhol wllbor prssur and rsrvoir prssur a r rspcivly, Q is h flow ra, μ is h injcd fluid viscosiy, k is formaion prmabiliy and H is h rsrvoir hicknss. W nglc h comprssibiliy of h rsrvoir fluid, so ha h formaion facor is qual o on. If ncssary, i can b asily incorporad in Eq. (1) as an addiional facor in fron of Q. Also, w adop h convnion ha injcion flow ra is posiiv. To accoun for formaion damag in clos viciniy of h wllbor, or h skin ffc, w assum som ffciv wllbor radius r 14 w. Th wll influnc zon is h zon nar h wllbor whr h fluid prssur changs apprciably du o h injcion. In h radial flow modl his influnc zon is circular. Th raio r /r w is bwn h wllbor radius and h radius of influnc, i.. h disanc from h wll o h par of h rsrvoir whr h prssur can b considrd undisurbd by h injcion or hld consan by ohr facors. In fac, quaion (1) also holds ru if h flow is no purly radial, in such a cas h prssurs hav o b avragd 13. Equaion (1) is basd on svral assumpions. Th fluid is homognous and incomprssibl. Th rsrvoir is vrically confind and uniform, boh wih rspc o h prmabiliy and h hicknss. Th rsrvoir is horizonal and graviy dos no affc h flow. Consqunly, h flow is radial. During h nir im of obsrvaions, h prssur a h disanc qual o r is consan, and his disanc islf is consan as wll. In pracic, no all, if any, of hs assumpions ar sricly saisfid. Th injcion inrval usually covrs mulipl zons of diffrn prmabiliy. Th gomric srucur of h flow can b disord by formaion hrogniy, inrfrnc bwn wlls, fracurs, c. Nvrhlss, Eq. (1) is of gra pracical imporanc, and in many cass i adqualy dscribs fluid injcion assuming som ffciv man formaion paramrs. Th cofficin μ r b = ln, () π kh rw or is invrs, is ofn usd o characriz wll prformanc. If h ras and prssurs ar almos consan ovr h obsrvaion im priod, hn b = p w Q p....(3) ha is b is h rciprocal of spcific wll injciviy 14. Applicaion of h las quaion can b limid by h inviabl flucuaions of h prssur and ra, and h lack of informaion abou h man ambin prssur p. Equaion (1) can b ingrad in im:

3 Silin al.: Monioring of Warflood Opraions: Hall s Mhod Rvisid 3 μ r p p dτ = ln Q d w τ π kh r ( )..(4) No ha h uppr limi of ingraion is variabl. As grows, h ingraion filrs ou shor-im flucuaions providing a mor robus procdur for valuaing h wll prformanc paramr b. Dno Π () = p ( τ ) dτ and () ( τ ) w w V = Q dτ (5) Th Hall plo analysis is jus ploing of h lf-hand sid of Eq. (4) vrsus h righ-hand sid, i.., ploing Π( ) p vrsus h cumulaiv injcion volum V(). Clarly, a a consan ambin rsrvoir prssur p, and consan cofficin b, h plo is a sraigh lin whos slop is qual o b. If h purpos of analysis is o compar formaion ransmissiviy bfor and afr wll ramn, hn h chang of h slop, or h cofficin b, should b valuad. Howvr, applicaion of Eq. (4) sill rquirs knowldg of p and an vidnc of consancy of b during h im of obsrvaion. Th following xampl illusras h imporanc of his informaion. Imagin a wll a quasi-saic injcion ovr a priod of 6 days. L boh h rsrvoir prssur and paramr b b consan ovr his priod of im. Assum ha war is injcd a a ra of 15 bbl/day and h wllbor injcion prssur is 15 psi during h firs 4 days. Th las wo days, h ra is incrasd o 3 bbl/day by incrasing injcion prssur o 17 psi. If h rsrvoir prssur is consan and qual p =14 psi, w immdialy obain ha h Hall plo is a sraigh lin and b=.5 psi-day/bbl. Howvr, if w plo Π() p vrsus cumulaiv injcion volum V() wih an incorrc rsrvoir prssur sima, hn h plo has a brak in h slop, Fig. 1. Thus, h only cas whn h Hall plo is a sraigh lin wih a variabl injcion ra is whn h rsrvoir prssur p is known and is xac valu is usd in Eq. (4). If prssur p is unknown, vn consan injcion condiions may rsul in a Hall plo wih a brak in h slop. Th magniud of h slop chang is a funcion of h discrpancy bwn h xac rsrvoir prssur and h prssur usd in Eq. (4). Th original papr by Hall 8 provids an xampl of analysis of wll daa bfor and afr a ramn assuming hr diffrn valus of p. Th sam daa yild hr diffrn slop changs afr wll ramn. Th injcion ra afr h ramn has changd. Thus, o wha dgr h slop chang is du o changs of h formaion propris afr h ramn and o wha dgr i is du o h lack of informaion abou h rsrvoir prssur, canno b ascraind from analyzing h plo alon. Th plo in Fig. 1 suggss ha if h formaion propris do no chang and h rsrvoir prssur also rmains h sam, hn h plo of Π()-p vrsus V() is a sraigh lin only if p=p. Thus, h formaion prssur p can b simad by slcing h valu of p, such ha h slop of h plo is consan. Blow, a mor lgan and robus rsrvoir prssur simaion procdur is discussd. Som auhors propos a simplifid procdur, whr h diffrnc p w -p is rplacd wih h wllhad prssur. Th xampl abov dmonsras ha h uncrainy of such analysis is no ngligibl. P rssur ingral, psi-day Cumulaiv injcion, bbl p =14 psi p =13 psi p =15 psi Fig. 1. Hall plo a consan formaion propris, bu wih diffrn rsrvoir prssurs. Th only sraigh lin wih h slop b=.5 psi-day/bbl on his plo corrsponds o h corrc rsrvoir prssur 14 psi. Hall Plo: Th Ky Paramrs To invsiga h impac of h ambin rsrvoir prssur and h radius of influnc on Hall plo analysis, synhic rsrvoir daa wr gnrad. Th forward simulaions wr prformd wih a modl usd in wll s analysis 11,1. This modl was buil upon h classical This prssur diffusion quaion o accoun for h impac of h sady-sa componn of flow drivn by h nar-wllbor rsrvoir prssur disribuion. This modl was slcd as h ool for forward simulaions bcaus i uss assumpions, which ar compaibl wih rgular injcion opraions, whr ransin flucuaions ar suprimposd upon long-im sady-sa flow. In his modl, h rsrvoir paramrs ar rprsnd as avrag ffciv quaniis, xacly as in h Hall mhod. Th modl has bn xnsivly vrifid agains ral fild daa. Wll s analysis producs a good-qualiy injcion prssur curv fi, which is sabl wih rspc o h slcion of h im inrval. Analysis of rgular opraions daa also producs consisn sabl simas 15. Thus, h following procdur is usd in his scion. Firs, h various opraion scnarios,.g., a sp injcion ra chang, ar simulad using h modl 11,1. Scond, h rsul is plod using h Hall plo mhod, and h signaurs of h influnc of diffrn paramrs ar obaind. I urns ou ha analysis of h fild daa prsnd in h las scion srongly confirms h simulaion rsuls. Th main quaion usd in modl 11,1 is

4 4 SPE whr B xp pw () τ = p + A Q w ( τ ) dτ τ Ei B + AQ 1 + AQ () s..(6) μ A = and 4π kh φμcr B = w.(7) 4k Equaion (6) assums radial flow in an infini rsrvoir. Th wllbor prssur a h bginning of h obsrvaion im inrval is dnod by p w =p( ), φ and c ar h formaion porosiy and bulk comprssibiliy. Th skin facor s is qual o ln(r w /r wb ), whr r wb is h acual wllbor radius 14. Paramr Q -1 is h ffciv injcion ra corrsponding o h nar-wllbor sady-sa formaion prssur disribuion rsuling from opraions prior o =. Th wllbor prssur a =, p w, is compud using h This soluion 16 ovr a subsanial im priod, and assuming undisurbd rsrvoir prssur as h iniial condiion. No ha p w, is no qual o h rsrvoir prssur du o h injcion conducd prior o =. In h simulaions, w hav assumd h rsrvoir prssur p qual o 95 psi and h ambin background quasi-sadysa injcion ra Q -1 qual o 15 bbl/day. W usd A=1. psi-day/bbl, B=.1 day. Ths valus of paramrs A and B do no dscrib any spcific formaion, bu hav ralisic ordrs of magniud. If h ra changs in sps, Fig. 4, h rspciv injcion prssur is no a picwis consan funcion of im Fig. 5. Nvrhlss, h Hall plo, Fig. 6, is almos picwis linar. Th rason is ha h soluion is basd on h xponnial ingral, B Ei...(8) whos cumulaiv ingral is clos o a linar funcion. Th linariy of a funcion of on variabl can b masurd by h magniud of is scond drivaiv. If his drivaiv is clos o zro, hn h funcion is almos linar. For h xponnial ingral (8), on has d B d B Ei d Ei d τ = τ d B (9) xp = Muliplicaion of boh sids of h las quaion by B maks i dimnsionlss B.(1) d d B B B Ei xp d = Th righ-hand sid of Eq. (1) is sandwichd bwn zro and B/(- ). Th lar xprssion dcays as - grows. Th paramr B is usually small, and h closnss of h cumulaiv ingral of h xponnial ingral (8) o a linar funcion rvals islf clarly. Fig. and Fig. 3 show xampl calculaions illusraing h commns abou h xponnial ingral. Alhough h xponnial ingral (8) is no a consan funcion, Fig., h plo of is cumulaiv ingral vrsus im is almos a linar du o h dcay of h scond im drivaiv (1) wih incrasing Ei(-B/) [days] Fig.. Exampl: h plo of xponnial ingral (8) wih B=.1[days] B Ei d [days] Fig. 3. Cumulaiv ingral of h xponnial ingral (8). Alhough h funcion is no consan, Fig., h cumulaiv ingral is almos a linar funcion

5 Silin al.: Monioring of Warflood Opraions: Hall s Mhod Rvisid 5 Fig. 6 shows h Hall plo of h gnrad daa. Th plo is pracically a sraigh lin (rd lin) only if p in Eq. (4) is xacly qual o h valu h rsrvoir prssur usd in h simulaions. If, insad of h xac valu, an incorrc rsrvoir prssur is usd in Eq. (4), h plo is a brokn lin (black and blu lins). Th cornrs on h lins corrspond o h momns whn h injcion ras ar changd by a sp incrmn. This picur is in full analogy wih h illusraion prsnd in Fig. 1, Q (bbl/day) T (day) Fig. 4. Sp incras of injcion ra P (psi) T (day) Fig. 5. Compud prssur buildup corrsponding o h ras in Fig. 4. Slop Plo: A Nw Wll Diagnosic Tool Visual inspcion of Hall s plo can b dciving. Th ingraion filrs ou prssur and ra flucuaions, which ar normally no oo larg in comparison wih h rspciv man valus. In his scion, w dmonsra ha hs visually almos imprcpibl Hall plo slop variaions can b analyzd o xrac vry imporan informaion abou h ffciv rsrvoir prssur and wll injciviy. As w hav dmonsrad, h corrc Hall plo rquirs knowldg of h man ambin rsrvoir prssur p. This prssur canno b masurd, so w us in our analysis an incorrc Hall plo, wih p s zro. To calcula h slop of his plo, on nds o valua h drivaiv Cumulaiv prssur diffrnc (psi day) dπ S = (11) dv Hall plo amb. p=95 (no rror) amb. p=855 (-1% rror) amb. p=76 (-% rror) Cumulaiv injcd volum (bbl) Fig. 6. Thr vrsions of h Hall plo analysis of h daa prsnd in Fig. 4 and Fig. 5. Only h xac rsrvoir prssur of 95 psi yilds a sraigh lin. Inaccura informaion abou h rsrvoir prssur rsuls in slop braks. From Eq. (5), pw S =. (1) Q From Eqs. (1) and (3), a quasi sady-sa condiions, p S = + b....(13) Q Th lar quaion implis ha h plo of S vrsus 1/Q is a linar funcion. Injcion ra Q and, by viru of Eq. (1), h slop S ar paramrs availabl from masurmn. Thrfor, boh h ambin rsrvoir prssur p and h wll injciviy paramr b ar obaind from Eq. (13) by linar fi of S vrsus 1/Q. This procdur is abbrviad as h slop plo analysis. Onc p is simad from h slop of h slop plo, i can b usd o cra h Hall plo according o Eq. (4). Fig. 7 prsns h slop plo analysis of h simulad daa displayd in Fig. 4-Fig. 6. Th plo is almos a sraigh lin brokn by h vrical jumps whr h injcion ra has sp changs. Ths paralll displacmns xprss changs in h injciviy paramr b. Sinc h formaion propris do no chang during hs simulaions, h variaions of b ar nirly du o h xpansions of h influnc zon radius causd by h incrasing injcion ra and prssur. Th slop sima of 957 psi is lss han 1% diffrn from h xac ambin prssur of 95 psi usd in hs simulaions. Lik Hall s plo, h lins in Fig. 7 canno b xacly sraigh bcaus of h characr of prssur variaions in Fig. 5. Howvr, hs variaions ar no larg in comparison wih avrag injcion prssur ovr h nir im inrval. Thrfor, visually, h lins ar almos sraigh du o nar-

6 6 SPE linariy of h ingral of h xponnial ingral funcion, as dmonsrad by Eqs. (9)-(1). P/Q (psi day/bbl) Slop plo x 1-3 1/Q (day/bbl) Las squard fiing: y = 957*x > ambin prssur~95 Fig. 7. Slop plo analysis of h forward simulaions prsnd in Fig. 4--Fig. 6. Smingly, Eq. (1) can b usd dircly for linar fiing by subsiuion of h masurd injcion ras and prssurs. Howvr, pracically, is mor suiabl for such analysis by h following rason. On h righ-hand sid of Eq. (1), h firs rm, h rsrvoir prssur, is usually largr han h scond rm, h addiional prssur buildup du o fluid injcion. This is why a linar fi of Eq. (13) in variabls S and 1/Q is mor sabl han ha of Eq. (1) in h original variabls p and Q. Thr is an imporan diffrnc bwn how h Hall plo and h slop plo display h daa. In a Hall plo, rgardlss of whhr h corrc rsrvoir prssur is usd in Eq. (4) or no, h horizonal axis (cumulaiv injcion) is a masur of lapsd im on injcion: poins o h righ always corrspond o lar ims han hos o h lf. Only if h wll is shu down and Q=, h poins on h x-axis collaps. In a slop plo, im is no involvd a all. Thrfor, injcion prssur injcion ra daa poins sparad by subsanial im can occur nx o ach ohr in a slop plo. In conras, conscuiv masurmns can b sparad from ach ohr if, for xampl, hr ar abrup flucuaions in h daa. In h Hall plo, im-avraging of h daa smoohs h curvs. In a slop plo, im-avraging may acually complica analysis and compromis h conclusions by inroducing arificial man daa poins. Wlls wih a flow gomry diffrn from radial flow,.g. fracurd wlls, can b analyzd in a similar mannr by rplacing h xponnial ingral by a diffrn wll funcion. In fac, sinc slop analysis is basd on h quasi-sady-sa quaion (13), i can b applid o any flow gomry wih an appropria modificaion of inrpraion of cofficins b. Th compuaional xampl abov simulas an idalizd siuaion of prfcly sady-sa flow in a homognous formaion. In raliy, hs assumpions can hold ru only on avrag. In fac, nighbor wlls may inrfr, h flow can b non-radial, c. Our xprinc wih analyzing daa from injcion wlls in Los Hills (s nx scion) shows ha in mos cass slop analysis producs an amazingly good sraigh lin. Fw oulirs may indica ransin flow. If a sysmaic dviaion occurs, i can b a sign of a problm. Th characr of his dviaion can b usd o diagnos h problm. Paramr b in Eq. (1) is a lumpd combinaion of h ransmissiviy, T=kh/μ, and h logarihm of raio of h radii, ln(r /r w ). If b is masurd in psi-day/bbl, ha corrsponds o prssurs masurd in psi and injcion ras masurd in bbl/day, hn kh Darcy- f 1.14 r (14) cp b μ ln r w Thus, if b~.14 [psi-day/bbl], r w ~.3 f, r ~11 f, hn T~6 [Darcy-f/cp]. If h injcd fluid is war, μ~1 cp, and h rsrvoir hicknss is abou 1 f, hn h ffciv prmabiliy of h rock is k=5 md. Assuming 3% porosiy and 1-6 psi -1 comprssibiliy, h prssur diffusion a h disanc 11 f is of h ordr of on hour. Thus, for sound analysis, h masurmns hav o b collcd ovr a im inrval much largr han 1 hour. Sinc h informaion abou rsrvoir rock propris is subjc o high uncrainy, longr im obsrvaion inrvals ar rcommndd for mor robus conclusions. Daild inrpraion of h obaind simas can b faciliad if addiional informaion is availabl. For xampl, h formaion ransmissiviy simad from ransin analysis 11, 1 can hlp o sharpn simas of h radius of wll influnc. An xampl of such a calculaion is prsnd in h nx scion. Exampls Jim, plas look if you can labora hr and hr This work is a par of h dvlopmn of auomaic warflood survillanc and conrol mhods and sofwar, and h ingraion of hs ools wih h Suprvisory Conrol and Daa Acquisiion (SCADA) sysm in Los Hills. Each war injcion sring is quippd wih a flow mr and prssur gaug. Th downhol injcion prssur is calculad by adding h hydrosaic prssur o h midpoin of prforaions o h gaug radings. Th viscous prssur drop in ubing flow is nglcd bcaus of h low flow ras. In fac, vn if his prssur drop wr of imporanc, bing proporional o h flow ra, i would b auomaically accound for hrough a small adjusmn o h skin facor, or h cofficin b in Eq. (). Daa from svral injcion wlls a Los Hills oil fild ar usd in his scion o illusra h slop mhod. Th prssurs and ras ar masurd and auomaically collcd vry minu. This high mporal rsoluion provids an xclln opporuniy for h subsqun daa analysis. Fig. 8 and Fig. 9 display injcion ras and injcion prssurs collcd from wll A ovr 6 days of rgular opraions. Excp a spik on h fourh day, hr ar no significan flucuaions in h flow rgim. Firs, h saring four days of daa wr slcd for h Hall plo analysis. Th im inrval was rducd o br illusra h apparanc of kinks in h plo causd by h injcion ra chang on h scond day, Fig. 8. On a longr im inrval, hs kinks bcom lss noicabl bcaus h

7 Silin al.: Monioring of Warflood Opraions: Hall s Mhod Rvisid 7 cumulaiv prssur ingral grows quickly and vn significan flucuaions bcom hiddn. Q[bbl/D] 1 8 Injcion Ras ha h nar-wllbor formaion may hav susaind damag. Howvr, w dmonsra blow ha i is no h cas. Th slop chang in Fig. 1 is causd nirly by h incorrc applicaion of Hall plo analysis rsuling from h lack of informaion abou h rsrvoir prssur, cf. xampls in Fig. 1 and Fig. 6 abov Cumulaiv Q [bbl] 8 6 Cumulaiv injcion Fig. 8. Wll A: Injcion ra daa collcd ovr 6 days 4 P[psi] 15 Injcion Prssurs Fig. 9. Wll A: Injcion prssur ovr 6 days. Th downhol prssur is calculad using h hydrosaic prssur incras. Ingral P[psi-day] Hall Plo Fig. 11. Wll A: Th cumulaiv injcion volum vrsus im. Fig. 1 displays h rsul of slop analysis applid o h daa shown in Fig. 8 and Fig. 9. Wih xcpion of vry fw oulirs, h daa poins (blu circls) ar closly alignd along h sraigh lin /Q+.19 [psi-day/bbl] (h rd lin). Sinc h daa in Fig. 1 do no involv im, nighbor poins in h plo can b rmo in im. To link h daa o h im, Fig. 13 displays h plo of h invrs injcion ra 1/Q vrsus. Th daa poins ar groupd ino four groups numbrd by h roman numrals I, II, III, and IV. Groups I and IV, which ar sparad in im, mrg ino on group in Fig. 13. In conras, Groups II and III ar clos in im bu ar sparad in Fig. 13. Slop[psi-day/bbl] 8 6 Slop plo I, IV II Cumulaiv Q [bbl] Fig. 1. Plo of h cumulaiv prssur vrsus cumulaiv injcion volum nglcing h ambin rsrvoir prssur, i.. p = in Eq. (4). Th blu lin is daa and h rd lin is linar fi. Th plo in Fig. 1 (h blu lin) consiss of wo sraigh sgmns and h chang of h slop a h join corrsponds o approximaly 4 barrls of cumulaiv injcion. Comparison wih Fig. 11 and, furhr, wih Fig. 8 and Fig. 9 shows ha his chang of slop occurrd whn h flow ra droppd by approximaly 5 bbl/day on h scond day. I is mping o conclud ha h slop chang in Fig. 1 is a sign 4 III /Q[Day/bbl] Fig. 1. Wll A: Th slop plo. Th blu dos ar daa and h rd lin is linar fi. Th ambin prssur sima, i.., h lin slop is psi, and h inrcp

8 8 SPE b is.19 psi-day/bbl. Th rsrvoir prssur sima of psi is an ffciv prssur ha drmins h rsrvoir rsisanc o h injcion. This sima characrizs h man rsrvoir prssur along h boundary of h domain influncd by Wll A. Th prsnd analysis is insufficin o rsolv h local prssur variaions causd by rsrvoir hrogniis. Howvr, p, along wih h cofficin b, carry imporan informaion abou h prssur disribuion in h rsrvoir. I can b usd o monior warflood prformanc, assss possibl rsrvoir comparmnalizaion, and drmin wll inracions wih naural or inducd fracurs and fauls. Analysis of h man prssur maps in juxaposiion wih h salli subsidnc imags 3 can b usd o s up snsibl arg ras for individual injcors. Such an analysis will b discussd lswhr /Q[Day/bbl] I 1/Ra II III IV Fig. 13. Wll A: Th invrs injcion ra, in day/bbl, vrsus im. Ingral P[psi-day] Hall Plo Subsiuion of rsrvoir prssur simas ino h Hall plo using Eq. (4) maks i a pracically sraigh lin, s Fig. 14. No ha h rang of valus along h vrical axis in Fig. 14 is subsanially smallr han ha in Fig. 1. Th rason is ha prssur ingraion wihou dducing h rsrvoir prssur sima rsuls in opraions wih larg numbrs. Thrfor, if h absolu valu of h dviaion bwn h sraigh rd lin and h plo in Fig. 1 wr rscald in rms of Fig. 14, his dviaion would show up in a vry xplici way. Thus, h absnc of h slop chang in Fig. 14 is du o h corrc accouning for h ambin rsrvoir prssur in Eq. (4). Applicaion of h slop analysis o h daa from wll B, Fig. 15 and Fig. 16, provids an xampl of diffrn kind. On h fourh day, afr h missing daa inrval, injcion ra had an abrup flucuaion, afr which, h ra coninud o flucua nar h sam avrag valu as during h firs 3 days of injcion. Th prssurs, howvr, slighly incrasd, saring from h 4 h day. Visually, h plo of h prssur ingral vrsus h cumulaiv injcion is almos a sraigh lin. Th rason for his is ha h fas growing prssur ingral hids h flucuaions. Afr applying h slop analysis, ffciv rsrvoir prssur has bn simad a 19 psi. This valus has bn subsiud in Eq. (4), and h corrcd Hall plo, Fig. 18 clarly shows an incras of h slop maning a rducion of injciviy. P[psi] Injcion Prssurs Fig. 15. Wll B: Th hisory of injcion prssur. No h prssur incrmn by h nd of h 4h day of injcion. Q[bbl/D] 15 1 Injcion Ras Cumulaiv Q [bbl] Fig. 14. Wll A: Th Hall plo afr corrcion for h simad ambin rsrvoir prssur. Th blu lin is basd on h daa and h rd lin is linar fi. Th rd and blu lins pracically coincid Fig. 16. Wll B: Th injcion ra rmains pracically h sam xcp los daa and a spik on h 4 h day of

9 Silin al.: Monioring of Warflood Opraions: Hall s Mhod Rvisid 9 injcion Ingral P[psi-day] Hall Plo P[psi] Injcion Prssurs Cumulaiv Q [bbl] Fig. 19. Wll C: A prssur fall-off curv amids rgular daa Q[bbl/D] 4 Injcion Ras Fig. 17. Wll B: Th ingrad prssur vrsus cumulaiv volum. Th prssur incrmn afr 4 days of injcion is pracically unnoicabl. Th daa (blu curv) and h fiing sraigh lin (rd) pracically coincid Ingral P[psi-day] Cumulaiv Q [bbl] Fig. 18. Wll B: Th corrcd Hall plo analysis: h injciviy rducion is clarly indicad by h incrmn of h slop. Th daa from wll C includ a prssur fall-off curv du o h injcion ra rducion from approximaly 35 bbl/day o bbl/day ovr h scond and hird days of injcion, Fig. 19 and Fig.. Th daa prsnd in Fig. 19 and Fig. can b analyzd using our ransin analysis mhod 11,1. This mhods aks as inpu h injcion ra and injcion prssur daa, and simas h formaion ransmissiviy, ambin rsrvoir prssur, and ffciv pr-s flow ra. Th prs flow ra Q -1, s Eq. (6), is a fiing paramr, bu i can b usd for an addiional vrificaion of h qualiy of fi Fig.. Wll C: An injcion ra rducion. Th mhod 11,1 includs slcion of h daa inrval o b analyzd, and a par of his inrval whr h prssur fiing will b prformd. Th daa inrval was slcd bwn 5 and 15 hours of injcion and is par saring a 45 hours was slcd for h fiing. Th rd dod curv in Fig. 1 is h rsul of fiing. Th daa ar machd wih high accuracy ovr a im priod longr han 4 days. Addiional confidnc in h daa fiing qualiy coms from h fac ha h ffciv flow ra 5 hours bfor injcion was simad a 346 bbl/day, ha is wihin 1% dviaion from h acual man injcion ra ovr h firs 5 hours of injcion. In fac, mulipl daa analyss on diffrn im inrvals using ODA 17 producd consisn rsuls. Ovr hs mulipl fiing runs, h man sima of ransmissiviy was abou 1.46 Darcy-f/cp and h ambin prssur was simad a 155 psi. Fig. shows h rsul of analysis of h sam daa from wll C using h slop plo mhod. Alhough h daa inrval includs prssur ransiion, mos of h daa poins (blu circls) ar nicly alignd along a singl sraigh maching lin (rd solid lin). Th group of oulirs corrsponds o h prssur fall-off, Fig. 19 and Fig. 1, whr h flow is ransin and, hrfor, Eq. (1) is no saisfid xacly.

10 1 SPE Prssur [psi] Tim [hours] Fig. 1. Prssur curv fiing. Th blu lin ar h daa and h dod rd lin is h fiing horical curv. Th daa bwn 5 and 15 hours of injcion ar usd for analysis, h fiing is carrid ou on h im inrval bwn 45 and 15 hours of injcion. Th fiing curv is xndd o h righ byond 15 hours. Slop[psi-day/bbl] Prssur falloff /Q[Day/bbl] Fig.. Th slop analysis yilds h rsrvoir prssur sima of 178 psi and h inrcp b=.5 psi-day/bbl. Th group of oulir daa poins corrsponds o h prssur falloff, s Fig. 19 and Fig. 1. Slop analysis yilds an ambin prssur sima of 178 psi, ha lss han 3% diffrn from h sima of 155 psi basd on analysis of h falloff curv. Using Eq. (14) and h sima of ransmissiviy obaind abov, w infr ha r 184 r..(15) w If w assum h ffciv wllbor radius of.5 f, hn h influnc radius is approximaly qual o 9 f. No, ha hs simas ar avrag ffciv valus and do no xclud significan local flucuaions of hs paramrs. Conclusions Th Hall plo analysis of injcion wll prformanc rquirs knowldg of rsrvoir prssur a h our boundary of h zon of influnc of h wll. Hr h zon of influnc of a wll is dfind as h rgion, whr h rsrvoir prssur apprciably changs du o h injcion. Nihr h prssur a h boundary of h zon of influnc nor h siz of his zon is availabl from masurmn. Thrfor, h sming simpliciy of Hall s plo analysis is ofn dciving. In paricular, h chang of slop of h Hall plo dos no ncssarily man changing formaion propris, bu can b a consqunc of h changing injcion ra and prssur only. A nw mhod, calld slop analysis, has bn proposd. This mhod uss flucuaions of h slop of h plo of cumulaiv prssur vrsus cumulaiv injcion volum o sima h ambin rsrvoir prssur and injciviy. Thrfor, h proposd analysis is basd on daa ha ar availabl from dirc masurmn and ar rouinly collcd in warflood opraions. Th obaind paramrs ar ffciv valus rprsning avrag rsrvoir propris and do no xclud significan local dviaions causd by h hrogniy of h formaion or wll inrfrnc. Th sima of h rsrvoir prssur obaind using our slop plo can b usd o corrc h Hall plo. Th slop mhod has bn sd and vrifid using simulad and fild daa. Using xampls, w hav shown ha his analysis, basd on h sady-sa flow modl, can b combind wih ransin analysis. Th good agrmn bwn h rsuls obaind by boh approachs brings confidnc abou h corrcnss of h rsuls and h validiy of h mhod in gnral. Join inspcion of h slop plo and ransin analysis maks possibl mor accura simas, which canno b obaind using ach mhod sparaly. Th simas of rsrvoir prssur obaind a ach wll can b mappd. Such a map in a projc or a fild scal provids valuabl informaion abou h rsrvoir condiions, including inracions bwn h wlls and naural and inducd fauls, and rsrvoir comparmnalizaion. Ths prssur maps ar discussd in dail lswhr. Th rsuls prsnd hr ar a par of h fild-scal warflood conrol in Los Hills dvlopd joinly by ChvronTxaco wih paricipaion of h Univrsiy of California, Brkly, and h Lawrnc Brkly Naional Laboraory. Incorporaion of hs rsuls ino injcion conrol dsign will b discussd lswhr. Acknowldgmns Th auhors hank ChvronTxaco for h prmission o publish his papr. Th Unid Sas Dparmn of Enrgy is acknowldgd for parial suppor for his work providd undr conrac No. DE-ACO3-76FS98 o h Lawrnc Brkly Naional Laboraory. Firs hr auhors apprcia parial suppor providd by ChvronTxaco, a mmbr of h U.C. Oil Consorium, Univrsiy of California a Brkly. Rfrncs 1.Talash, A.W., "An Ovrviw of Warflood Survillanc and Monioring,". Journal of Prolum Tchnology, 1988(Dcmbr): p Brink, J.L., T.W. Pazk, D.B. Silin, and E.J. Filding. Los Hills Fild Trial - Incorporaing Nw Tchnology for Rsrvoir Managmn. in SPE Annual Tchnical Confrnc and Exhibiion.. San Anonio, Txas: SPE. 3.Pazk, T.W., D.B. Silin, and E. Filding. Us of Salli Radar Imags in Survillanc and Conrol of Two Gian Oilfilds in California. SPE7161. in 1 SPE Annual Tchnical Confrnc and Exhibiion. 1. Nw Orlan, LA: SPE.

11 Silin al.: Monioring of Warflood Opraions: Hall s Mhod Rvisid 11 4.Earloughr, R.C., Advancs in Wll Ts Analysis. Monograph Sris. Vol , Nw York: Sociy of Prolum Enginrs. 5.Pazk, T.W. and D.B. Silin. Fluid Injcion ino a Low- Prmabiliy Rock - 1. Hydrofraur Growh. in SPE/DOE Elvnh Symposium on Improvd Oil Rcovry Tulsa, Oklahoma: SPE, Inc. 6.Silin, D.B. and T.W. Pazk, "War injcion ino a lowprmabiliy rock - : Conrol modl,". Transpor in Porous Mdia, 1. 43(3): p Silin, D.B. and T.W. Pazk, "Conrol modl of war injcion ino a layrd formaion,". SPE Journal, 1. 6(3): p Hall, H.N., "How o Analyz Warflood Injcion Wll Prformanc,". World Oil, 1963(Ocobr): p Bull, R.S., H. Kazmi, and F.H. Pomann. Analyzing Injciviy of Polymr Soluions Wih h Hall Plo SPE in SPE Annual Tchnical Confrnc and Exhibiion Dallas, TX: SPE. 1.Honarpour, M.M. and L. Tomusa. Injcion/Producion Monioring: An Effciv, Mhod for Rsrvoir Characrizaion SPE6. in SPE/DOE Svnh Symposium on Enhancd Oil Rcovry Tulsa, OK: SPE. 11.Silin, D.B. and C.-F. Tsang, "A wll-s analysis mhod accouning for pr-s opraions,". SPE Journal, 3(March): p Silin, D.B. and C.-F. Tsang, "Esimaion of Formaion Hydraulic Propris Accouning for Pr-Ts Injcion or Producion Opraions,". Journal of Hydrology,. 65(1): p Muska, M., Th Flow of Homognous Fluids hrough Porous Mdia. 1946, Ann Arbor, MI: J.W.Edwards, Inc. 14.Mahws, C.S. and D.G. Russll, Prssur Buildup and Flow Tss in Wlls. 1967, Nw York, NY: SPE of AIME. 15.Silin, D.B., C.-F. Tsang, and H. Grrish. Rplacing annual shu-in wll ss by analysis of rgular injcion daa: fild-cas fasibiliy sudy. in Undrground Injcion Scinc and Tchnology. Scond Inrnaional Symposium. 3. Brkly, CA: LBNL. 16.This, C.V., "Th Rlaionship Bwn h Lowring of h Pizomric Surfac and h Ra and Duraion of Discharg of a Wll Using Ground-War Sorag,". Transacions AGU, : p Silin, D.B. and C.-F. Tsang, "ODA, Opraions Daa Analysis,". 1, Lawrnc Brkly Naional Laboraory: Brkly. SI Mric Convrsion Facors acr E+3 = m Darcy E-13 = m bbl E-1 = m 3 cp 1.* E-3 = Pa s f 3.48* E-1 = m f E- = m 3 in..54* E+ = cm md E-4 = µm psi E+ = kpa Nomnclaur A = fiing paramr, psi-day/bbl B= fiing paramr, day c = fluid/formaion comprssibiliy, psi -1 H= rsrvoir hicknss, f k = absolu rock prmabiliy nar h wllbor, Darcy p w = wllbor prssur, psi p = avrag prssur in h formaion, psi p w = wllbor prssur a h bginning of daa inrval, psi r = influnc zon radius, f r wb = wllbor radius, f r w = ffciv wllbor radius, f Q= injcion ra, bbl/day Q -1 = pr-s injcion/producion ra, bbl/day S= plo slop, psi s= skin facor, dimnsionlss φ = porosiy, dimnsionlss μ = fluid viscosiy, cp