THE USE OF INFLOW PERFORMANCE RELATIONSHIPS TO IDENTIFY RESERVOIR RESPONSE DURING PRODUCTION TESTS IN A GEOTHERMAL WELL

Transcription

1 PROCEEDINGS, Thirty-Scond orkshop on Gothrmal Rsrvoir Enginring Stanford Univrsity, Stanford, California, January -4, 7 SGP-TR-183 THE USE OF INFLO PERFORMANCE RELATIONSHIPS TO IDENTIFY RESERVOIR RESPONSE DURING PRODUCTION TESTS IN A GEOTHERMAL ELL Aragón, A. 1, Suárz, M. C., Moya, S. 3, Izquirdo, G. 1 1 Instituto d Invstigacions Eléctricas Av. Rforma 113, Col. Palmira Curnavaca, Morlos, 649, México -mail: aaragon@ii.org.mx; gim@ii.org.mx Univrsidad Michoacana d San Nicolás Hidalgo Fac. D Cincias Físico-Matmáticas, Edif. B. Ciudad Univrsitaria Morlia, Michoacán, 58, México -mail: mcsa5@gmail.com 3 Cntro Nacional d Invstigación y Dsarrollo Tcnológico Av. Palmira, Esquina Call Apatzingan, col. Palmira Curnavaca, Morlos, 649, México -mail: slmoya@cnidt.du.mx ABSTRACT Th bhavior of four inflow prformanc rlationships ar analyzd and discussd. Two of thm ar dvlopd for ptrolum systms and two othrs ar dvlopd for gothrmal fluid containing high and low salinity rspctivly. A mthodology to dtrmin th imum flow rat ( ) that a wll can produc for a spcific stag of its productiv lif, using ths inflow rlationships is prsntd. Also it is showd th way to idntify th intrvals of th dimnsionlss prssur valus ( ), for which th imum flow rat can b considrd as stabl and as a rsrvoir rspons according to its bottom flowing prssur (p ). Application of this mthodology to four cass of production tst in wlls was carrid out, founding that th intrvals of valus whr th stabilizd flow is idntifid is a function of th magnitud of th wll flow capacity. INTRODUCTION Rsrvoir nginring for wll charactrization uss among othr tools, th inflow curvs also known as IPR curvs (Inflow Prformanc Rlationships). Th inflow curv of a wll is quivalnt to th output curv but it is masurd at bottom hol conditions. Both curvs ar individuals for ach wll and vary with th productiv lif of th wll. Th output curvs ar obtaind from th masurmnts at surfac conditions of th flow and prssur. Th original application of inflow curvs was don in th ptrolum industry (Muskat, 1937; Evingr and Muskat, 1937; Hornr, 1951; Gilbrt, 1954; llr, 1966; Vogl, 1968; iggins, 1994). Also svral authors (Grant t al., 198; Kjaran and Elliasson, 198; Garg and Riny, 1984; Chu, 1988; Jams, 1989; Gunn and Frston, 1991a) bgan to utiliz th tchniqu of output curvs in gothrmal rsrvoirs. Also diffrnt gothrmal inflow prformanc rlationships wr dvlopd assuming th fluid as: a) pur watr (Iglsias and Moya, 199), b) a mixtur H O-CO (Moya, 1994; Moya t al., 1998), c) a trnary mixtur H O-CO -NaCl with low salinity (Montoya, 3), and d) a trnary mixtur H O-CO - NaCl with high salinity (Mza, 5). INFLO RELATIONSHIPS Thr ar many applications of inflow rlationships and on of thm is th dtrmination of th imum flow ( ) that a wll can produc. Th valu of th imum flow is usful in th dsign of xploitation, and to fix th rfrnc valu from which it can idntify th dclin in th wll production. Th inflow curvs ar rlatd by thir rspctiv dimnsionlss rlations, which utiliz th variabls of flow and prssur obtaind in a wll tst production. Th dimnsionlss xprssions of ths variabls ar: p D D p = p = (1) ()

2 hr p is th bottom flowing prssur, p is th static prssur of formation, is th flow and is th imum flow that th wll can produc. Th inflow prformanc rlationships us th variabls of flow and prssur, which ar masurd in a production tst of th wll. Making ths variabls in thir dimnsionlss form, w can dtrmin th charactristic valu (static prssur or imum flow that th wll can produc). Among th divrs xisting inflow rlationships in th ptrolum tchnology, four wr slctd to us in this work. Two of thm ar from ptrolum nginring (Vogl, 1968; and iggins, 1994), whos rspctiv xprssions ar: ( Q Q o o ) Qw ( Q ) w = 1.. = (3) For high salinity = (6) Figur 1 shows a comparison of th four inflow rlationships analyzd in this work (Vogl, 1968; iggins, 1994; Montoya, 3; Mza, 5). Thr of thm hav similar bhavior; only on, which is th proposd by iggins (1994), dviats from thr othrs. Th imum prcntag dviations of ths thr rlations vary from 7.1 to 9. %, and ths occur for valus of from.4 to.6. Tabl 1 shows th rsults of D obtaind using th thr rlations and th prcntag diffrncs among ths. 1 (4) hr Q o is th oil flow rat and (Q o ) is th imum oil flow rat, and Q w is th watr flow rat and (Q w ) is th imum watr flow rat From th diffrnt inflow rlationships dvlopd for gothrmal rsrvoirs, in this work w us two of thm. On xprssion (Eq. 5) assums th fluid is a trnary mixtur (H O-CO -NaCl) with low salinity (lss than 5 % of mass fraction in liquid phas) (Montoya, 3); Scond xprssion (Eq. 6) is dvlopd assuming th sam trnary mixtur but for high salt contnt (3% of mass fraction in th liquid phas) including prcipitation conditions (Mza, 5). Such rspctiv xprssions ar: For low salinity = (5) Vogl (1968) iggins (1994) Mza (5) D Figur 1. Comparison of th bhavior of inflow rlationships usd in this work. pd D Diffrncs Vogl % (1968) Mza (5) Tabl 1. Maximum prcntag diffrncs dtrmining D with thr inflow rlationships.

3 Ordinarily th production tsts of wlls incorporatd to continuous xploitation ar carrid out with only thr or four masurmnts. Th rquird tim to obtain conditions of th stabilization in such masurmnts is a rason for which fw data ar obtaind. Thrfor it turns out appropriat, to idntify th answr of th rsrvoir to changs in th production outputs. It is fasibl to utiliz th inflow rlationships and th linking among th prssur dimnsionlss ( ) and th imum flow ( ) that is obtaind from its application in fild cass. Th objctiv is to idntify th avrag stabilizd that is rachd with th diffrnt opnings (or discharg diamtrs), for which th corrsponding valu of is obtaind. This valu is rlatd to th bottom hol prssur and to th discharg diamtrs. METHODOLOGY Th st of valus that ar rquird for th application of th inflow rlationships ar th flow and th bottom hol prssur (p ) of th wll during a production tst. Nvrthlss, du to th mass that th wll dischargs, it is a complicatd task to masur its bottom conditions during a production tst. Ordinarily flow simulators in wlls ar usd to dtrmin bottom conditions from thir corrsponding surfac masurmnts. It is rcommndd to hav a flow simulator applicabl to th charactristics of th fild in ordr to obtain rsults with confidnc. Th routin application of th inflow rlationships assums knowldg of th static prssur of th formation bfor th production tst. Subsquntly th valu of th bottom prssur (p ) is usd for a masurd flow and both valus in th corrsponding xprssion (Eqs. (3), (4), (5) or (6)) ar incorporatd. Th rsult is th dimnsionlss flow ( D ). Subsquntly, applying Eq. (), th imum flow ( ) that th wll can produc, can b dtrmind A graph of against is built and th stabilizd valu of th imum flow is idntifid. From th sam plot, th rank of valus of for th stabilizd flow can b dtrmind. APPLICATIONS production tst of wll M-, ar at wllhad conditions. Thir corrsponding output curvs ar shown in Figs. 3 and 4. Using wll flow simulators (Goyal t al., 198; Gunn and Frston, 1991b; Moya t al., 3) th rspctiv bottom hol conditions wr dtrmind, rsulting in thir inflow curvs which ar shown in Figs. 5 and 6. p (t/h) Figur. Inflow curv of wll Carry City (Gallic and iggins, 1999). p wh (t/h) Figur 3. Production output curvs of wll M-11, from production tst conductd in 1979 and 1987 (Ribó, 1989) Th mthodology dscribd abov, was applid to data of production tsts of th Carry City wll (Gallic and iggins, 1999), and of th Crro Prito wlls, M-11 and M- (Ribó, 1989). Th prssur valus rportd by Gallic and iggins (1999) corrspond to th bottom conditions of th Carry City wll, and in th Fig. its inflow curv is shown. Th rportd data (Ribo, 1989) for th two production tsts of wll M-11 (in 1979 and 1987) and on

4 P wh 6 5 Using th inflow data of ach production tst in th four inflow rlationships analyzd in this work (Eqs. 3, 4, 5 and 6), thir rspctiv valus of imum flow rat ( ) wr dtrmind. Graphs of against thir corrsponding valus of dimnsionlss prssur ( ) wr built. Th dtrmind as a rspons of th rsrvoir rsults from th avrag valu of calculatd in its stabilization intrval (Figs. 7, 8, 9 and 1 for ach production tst) Mza (5) iggins (1993) Vogl (1968) (t/h) Figur 4. Output curv of wll M- (Ribó, 1989) p Figur 7. Bhavior of against using th four inflow rlationships with Carry City wll data. 6 8 (t/h) Figur 5. Inflow curvs of wll M-11, dtrmind from production tst data of 1979 and Mza (5) iggins (1993) Vogl (1968) 8 P 15 6 Figur 8. Bhavior of against using th four inflow rlationships with production tst data of 1979 from wll M (t/h) Figur 6. Inflow curv of wll M-, dtrmind from production tst data of In th Tabl th avrag valus of ar shown in th intrval in which thy rmain stabl. In th sam tabl, th prcntag diffrncs in th calculation of this valu ar includd for th four rlations and liminating th rlation with which

5 gratr dviations ar obtaind, that is that of iggins (1994). (t/h) Mza (5) iggins (1993) Vogl (1968) Th dtrmind valu of (Tabl ) corrsponds to th imum flow that th wll can produc for th conditions in which th tst is prformd and is th on that is utilizd for th dsign of fild xploitation. From th four inflow rlationships usd in this work, it is found that th proposd rlation by iggins (1994) is th on that shows gratr dviation for th calculation of D and by consqunc in th calculation of (Tabl ). Th obtaind dviation in th rsults with th rlation proposd by iggins (1994) is rlatd mainly with th supposition of th typ of fluid with rspct to th typ of fluid considrd in th othr thr rlations. Th supposition of iggins rlation dos not considr prsnc of gas in th flow. Figur 9. Bhavior of against using th four inflow rlationships with production tst data of 1987 from wll M Mza (5) iggins (1993) Vogl (1968) Th prcntag dviation in calculation of (Tabl ) is a function of th magnitud of th flow valu. From Eq. it can b sn in Tabl that is rlatd to p, and it is function of th discharg diamtr. By idntifying th intrvals in which th stability of with rspct to is rachd, it is fasibl to idntify th appropriat conditions that th discharg through a spcific opning corrsponds to optimal rsrvoir production. CONCLUSIONS (t/h) 9 8 A rvision of four inflow rlationships was conductd, two originally dvlopd for ptrolum systms and two considring th gothrmal fluid as a trnary mixtur (H O-CO -NaCl) with high and low salinity, rspctivly. 7 6 Figur 1. Bhavior of against using th four inflow rlationships with production tst data of 1985 from wll M-. A mthodology to dtrmin from th inflow rlationships and its corrsponding valu of is prsntd. From th obtaind rsults it is possibl to idntify th ranks of valus for which valus ar stabilizd. (t/h) Diffrnc (%) ll Vogl (1968) iggins (1994) Montoya (3) Mza (5) Not including Including iggins iggins Carry City M-11 (1979) M-11 (1987) M Tabl. Avrag valus of and prcntag diffrncs in th intrval of stability, dtrmind with th four inflow rlationships usd in this work. RESULTS AND DISCUSSION Th intrvals of valus for which valus ar stabilizd, is a function of th magnitud of wll flow capacity. From th four inflow rlationships utilizd in this work, imum flows calculatd with th four quations ar rlatd to corrsponding diamtrs of opning through th dimnsionlss prssur ( ). AKNOLEDGEMENTS

6 Th authors xprss thir gratitud to Instituto d Invstigacions Elctricas by th support to publish this work. REFERENCES Chu, M. H. (1988), Inflow prformanc rlationships for goprssurd gothrmal wlls, Gothrmal Rsourcs Council Transactions, 1, Evingr, H. H., Muskat, M. (194), Calculation of thortical productivity factor, Trans., AIME, No. 146, Gallic, F., iggins, M. (1999), A comparison of two-phas inflow prformanc rlationships, SPE Mid-Continnt Oprations Symposium, Oklahoma City, U.S.A., Garg, S. K., Riny, T. D. (1984), Analysis of flow data from th DO/DOE L. R. Swzy No. 1 wll Topical Rport, DOE/NV/115-5, La Jolla, CA. E.U.A., Gilbrt,. E. (1954), Flowing and gas-lift wll prformanc, Drilling and Production Pract., API, 16 p. Goyal, K. P., Millr, C.., Lippman, M. J. (198), Effct of masurd wllhad paramtrs and wll scaling on th computd downhol conditions in Crro Prito lls Proc. 6 th orkshop on Gothrmal Rsrvoir Enginring, Stanford Univrsity, California, U.S.A., Gunn, C., Frston, D. (1991a), Applicability of gothrmal inflow prformanc and quadratic drawdown rlationships to wllbor output curv prdiction, Gothrmal Rsourcs Council Transactions, 15, Gunn, C., Frston, D. (1991b), An intgratd stady-stat wllbor simulation and analysis packag, Proc. 13 th Nw Zaland Gothrmal orkshop, Nw Zaland, Grant, M. A., Donaldson, I. G., Bixly, P. F. (198), Gothrmal rsrvoir nginring, Acadmic Prss, Nw York, U.S.A., 117 p. Hornr, D. R. (1951), Prssur build-up in wlls, Proc. Third orld Ptrolum Congrss, Sction II, E. J. Brill Lidn, Iglsias, E. R., Moya, S. L. (199), Gothrmal inflow Prformanc rlationships, Gothrmal Rsourcs Council Transactions, 14 part II, p Jams, R. (1989), On curv fits all, Proc. 14 th orkshop on Gothrmal Rsrvoir Enginring, Stanford Univrsity, California, U.S.A., Kjaran, S. P., Elliasson, J. (198), Gothrmal rsrvoir nginring, Lctur nots, Univrsitty of Icland, Rykjavik Icland, 36. Mza, C. O. (5), Efcto d la prcipitación d sals n l diagnóstico d prmabilidads rocosas, Tsis d mastría, CENIDET (Cntro Nacional d Invstigación y Dsarrollo Tcnológico) SEP, 17 p. Montoya, D. (3), Estimación d prmabilidads d yacimintos gotérmicos mdiant la aplicación d curvas tipo d influjo gotérmico, Tsis d mastría, CENIDET (Cntro Nacional d Invstigación y Dsarrollo Tcnológico) SEP, 11 p. Moya, S. L. (1994), Efctos dl bióxido d carbono sobr l transport d masa y nrgía n yacimintos gotérmicos, Tsis Doctoral, División d Estudios d Posgrado, Facultad d Ingniría, Univrsidad Nacional Autónoma d México, 4 p. Moya, S. L., Aragón, A. A., Iglsias, E. R., Santoyo, E. (1998), Prdiction of mass dlivrability from a singl wllhad masurmnt and gothrmal inflow prformanc rfrnc curvs, Gothrmics, 7 3, Moya, S. L., Urib, D., Montoya, D. (3), Computational systm to stimat formation prmabilitis and output curvs of gothrmal wlls, Computr and Goscinc, 9, Muskat, M. (1937), Th flow of homognous fluids through porous mdia, Mc Graw Hill Book Company, Inc., Nw York, U.S.A., Ribó, M. O. (1989), Análisis d prubas d prsión n pozos d Crro Prito, Procdings symposium in th fild of gothrmal nrgy, Agrmnt CFE- DOE (Comisión Fdral d Elctricidad d México Dpartmnt of Enrgy of Unitd Status of Amrica), San Digo California, U. S. A, Vogl, J. V. (1968), Inflow prformanc rlationships for solution gas driv wlls, Journal Pt. Tch. (SPE 1476) Annual Fall Mting of Socity of Ptrolum Enginrs, Dallas Txas, U.S.A., llr,. T. (1966), Rsrvoir prformanc during two-phas flow, Journal Pt. Tch., 46. iggins, M. L. (1994), Gnralizd inflow prformanc rlationships for thr-phas flow, SPE Production Oprations Symposium (SPE 5458), Oklahoma City, U.S.A.,