CHAPTER 3 MECHANISTIC COMPARISON OF WATER CONING IN OIL AND GAS WELLS Wtr coning in gs lls hs n undrstood s phnomnon similr to tht in oil ll. In contrst to oil lls, rltivly f studis hv n rportd on spcts of tr coning in gs lls. Muskt (1982) livd tht th physicl mchnism of tr coning in gs lls is idnticl to tht for oil lls; morovr, h sid tht tr coning ould cus lss srious difficultis for lls producing from gs zons thn for lls producing oil. Triml nd DRos (1976) supportd Muskt s thory ith tr coning dt nd simultion for Todhuntrs Lk Gs fild. Thy clcultd tr-fr production rts using th Muskt-Wyckof (1935) modl for oil lls in conjunction ith th grph prsntd y Arthurs (1944) for coning in homognous oil snd. Th rsults r comprd ith fild study ith commrcil numricl simultor shoing tht th rts clcultd ith th Muskt-Wyckof thory r 0.7 to 0.8 thos of th coning numricl modl for 1-yr priod. Th ojctiv of this study is to compr tr coning in gs-tr nd oil-tr systms. Anlyticl nd numricl modls r usd to idntify possil diffrncs nd similritis tn oth systms. 3.1 Vrticl Equilirium A hydrocron-tr systm is in vrticl quilirium hn th prssur drdon round th llor is smllr thn th prssur grdint gnrtd y th dnsity contrst tn th hydrocron nd tr t th hydrocron-tr intrfc. Eqution 3.1 shos th prssur grdint for gs-tr systm. 30
p = 0.433( γ γ ) h g g (3.1) Whr p is prssur grdint (psi), γ is tr spcific grvity, γ g is gs spcific grvity, nd h g- is th vrticl distnc from th rfrnc lvl to th gs-tr intrfc, normlly from th ottom of th ll s compltion to th gs/tr contct (ft). Vrticl quilirium concpt is th s for criticl rts clcultions. Criticl rt, in gs-tr systms, is dfind s th mximum rt t hich gs lls r producd ithout production of tr. 3.2 Anlyticl Comprison of Wtr Coning in Oil nd Gs Wlls for Wtr Brkthrough To hydrocron systms, oil nd gs, in vrticl quilirium ith ottom tr r considrd to compr tr coning in oil nd gs lls for rkthrough. Th to systms hv th sm rsrvoir proprtis nd thicknss, nd r prfortd t th top of th producing zon. ll r= 0.5 ft K= 100 md φ=0.2 P=2000 psi T= 112 o F 50 ft 20 ft Oil Gs µ= 1.0 cp 0.017 cp ρ= 0.8 gr/cc 0.1 gr/cc µ=0.56 cp ρ= 1.02 gr/cc tr r= 1000 ft Figur 3.1 Thorticl modl usd to compr nlyticlly tr coning in oil nd gs lls for rkthrough. 31
Figur 3.1 shos sktch of th rsrvoir systm including th proprtis nd dimnsions. Th mthmticl clcultions r includd in Appndix A. A prssur drdon ndd to gnrt th sm sttic tr con lo th pntrtions, nd th fluid rt for ch systm s clcultd. For th systm of oil nd tr nd con hight of 20 ft, prssur drdon qul to 2 psi is ndd, nd th oil production rt is 6.7 st/d. In th cs of gs-tr systm, for th sm 20 ft hight of tr con 8 psi prssur drop is ndd, nd th gs production rt of 1.25 MMscfd. From this first simpl nlysis it is vidnt tht it is possil to hv stl tr con of ny givn hight in th to systms (oil-tr nd gs-tr). For th sm con hight in vrticl quilirium, prssur drop in th gs-tr systm is four tims grtr thn th prssur drop in th oil-tr systm. Thr is ig diffrnc in th fluids production rt for gs-tr nd oil-tr systm. On th sis of British Thrml Units (BTU), th nrgy contnt of on Mscf of nturl gs is out 1/6 of th nrgy contnt of on rrl of oil (Economids, 2001). For this xmpl, th 1.25 MMscf r quivlnt to th BTU contnt of 208 rrls of oil. Thrfor, for th sm tr con hight, it ould conomiclly possil to produc gs-tr systms t th gs rt lo criticl. Hovr, in most css it ould not not conomiclly possil to produc oiltr systms ithout tr rkthrough. 3.3 Anlyticl Comprison of Wtr Coning in Oil nd Gs Wlls ftr Wtr Brkthrough Th ojctiv is to compr th shp of oil-tr nd gs-tr intrfcs t th llor ftr tr rkthrough. Aftr th tr rkthrough, thr is strtifid inflo of oil or gs ith th tr covring th ottom sction of th ll compltion. Agin, to systms hving th sm rsrvoir proprtis nd thicknss r comprd (oil- 32
tr nd gs-tr). Both systms r totlly pntrtd. An qution dscriing intrfc shp s drivd using th ssumptions of Muskt (1982). Figur 2 shos sktch of th thorticl modl, nd Appndix A givs th drivtion nd mthmticl computtions. In rlity th rsulting qutions ill not dscri prfctly th inflo t th ll. Hovr, thy r usful to compr th coning phnomnon in oil-tr nd gs-tr systms. ll P h P oil / gs y y=? tr r r Figur 3.2 Thorticl modl usd to compr nlyticlly tr coning in oil nd gs lls ftr rkthrough. Th rsulting qutions for th tr coning nlysis r: For th oil-tr systm th intrfc hight is dscrid s, h y = (3.1) + 1 hr, nd r constnts dscrid s, = Q µ o o 2πφkh Qµ =. 2πφkh h y =. (3.2) y 33
y = For th gs-tr systm th intrfc hight is rprsntd s, hp [( / ) + p] (3.3) hr,, nd p r clcultd using: Qg µ g =, 2πφkh Qµ =, nd 2πφkh [ 1 ( y / h)] = * p (3.4) ( y / h) r ln r 1 = p p p + / ln.(3.5) p + / From Eqution 3.1 it coms ovious tht hn th ll s inflo of oil nd tr is strtifid so th uppr nd ottom sctions of compltion produc oil nd tr rspctivly, undr stdy stt flo conditions th intrfc tn th to fluids is constnt nd prpndiculr to th llor cus th prmtr dscriing th intrfc hight r ll constnt nd dpnds on th systm gomtry. For th gs-tr systm, nvrthlss, th intrfc hight dpnds on th gomtry of th systm, nd th prssur distriution in th rsrvoir (Eqution 3.3). In ordr to dmonstrt th modl for gs-tr systms dscriing th intrfc tn gs-tr, on xmpl s solvd. Th systm dt r s follo: p = 2000 psi r = 2000 ft r = 0.4 ft h = 50 ft y = 40 ft µ = 0.498 cp B = 1.0 k = 100 md φ = 0.25 µ g = 0.017 cp Th procdur is s follos: 1. Assuming vlu for th prssur drdon (300 psi). 2. Clculting th floing ottom hol prssur ( p = p p = 2000 300 = 1700) ssuming tht p is constnt long th llor. 34,
3. Computing th tr flo rt (Q ) using Drcy s l qution (Krft nd Hkins, 1991): Q 0.00708kh ( p p = µ B ln( r / r ) ) = 0.00708*100 * 40 * (2000 0.498*1.0 * ln(2000 / 0.4) 1700) = 2000 4. Clculting /, using EqutionA-16 in Appndix A: 1 ( y / h) p ( y / h) = = [ 1 (40 / 50) ] * 2000 (40 / 50) = 500, hich is constnt for th systm nd indpndnt for th gs rt. 5. Finding Q g, from Eqution A-15 in Appndix A: Qg µ g = Q µ Q g *0.017 *5.615 500 = Q g = 5.22 MMscf/d 2000*0.498 Not tht WGR is constnt for th systm nd dpnds only on th systm gomtry (y, h) nd prssur driv (p ). 6. Computing 1/, using Eqution A-17 in Appndix A: 1 = ( p p r ln r p ) ln p + ( / ) + ( / ) 1 = 6000 ln 4 = 0.031 2000 + 500 (2000 1700) ( 500) ln 1700 + 500 7. Assuming prssur vlus tn p nd p, rdii r nd th gs-tr profil y r clcultd, using Equtions A-14 nd A-18 rspctivly in Appndix A. This is th gs-tr intrfc profil. Th qution usd to clcult prssur distriution in th rsrvoir is: 35
r ln r 1 = p p p + / ln p + / 6000 ln r 2000 + 500 = 0.031 2000 p 500ln p + 500 Th qution usd to clcult th gs-tr intrfc profil (hight) is: y = hp [( / ) + p] y 50* = 500 p p [ + ] (Not tht this prssur distriution dos not dpnd on vlus of flo rt ut only on thir rtio.) Rpting th sm procdur for th oil-tr systm: ( h y (50 40) 40 From Eqution A-22 in Appndix A: = = = 0. 25 Using Eqution A-26 in Appndix A: y = = = 40 y ) h + 1 50 (0.25 + 1) For th oil-tr systm y rmins constnt ( y = 40) nd indpndnt from rdius. Fluids Intrfc Hight (y) vs rdii (r) Fluids Intrfc Hight (ft) 40.2 40.0 39.8 39.6 39.4 39.2 39.0 38.8 38.6 38.4 0 500 1000 1500 2000 2500 Rdii (ft) gs-tr systm oil-tr systm Figur 3.3 Shp of th gs-tr nd oil-tr contct for totl prfortion. 36
Figur 3.3 shos th rsulting profils of th fluid intrfc in gs-tr nd oiltr systms. Aftr rkthrough, th oil-tr intrfc t th ll s compltion is horizontl, hil th gs-tr intrfc tnds to con into th tr. For this xmpl th totl lngth of th gs con is 1.4 ft. 3.4 Numricl Simultion Comprison of Wtr Coning in Oil nd Gs Wlls ftr Wtr Brkthrough On numricl simultor modl s uilt to confirm th prvious finding out th con shp round th llor. Figur 3.4 shos th numricl modl ith its proprtis. Tl 3.1 shos fluids proprtis usd, nd Appndix B contins Eclips dt dck for th modls. k= 10 md SGgs= 0.6 φ=0.25 APIoil= Pinitil=2300 psi T= 110 o F Wll, r = 3.3 in Top: 5000 ft 100 lyrs of 0.5 ft thick Gs or Oil 50 ft 9 lyrs 5 ft thick, nd on lyr 550 ft thick. Wtr (W) 5000 ft 600 ft Figur 3.4 Numricl modl usd for comprison of tr coning in oil-tr nd gs-tr systms. 37
Tl 3.1 Gs, tr nd oil proprtis usd for th numricl simultor modl Gs Dvition Fctor nd Viscosity (Gs-tr modl) Prss Z Visc 100 0.989 0.0122 300 0.967 0.0124 500 0.947 0.0126 700 0.927 0.0129 900 0.908 0.0133 1100 0.891 0.0137 1300 0.876 0.0141 1500 0.863 0.0146 1700 0.853 0.0151 1900 0.845 0.0157 2100 0.840 0.0163 2300 0.837 0.0167 2500 0.837 0.0177 2700 0.839 0.0184 3200 0.844 0.0202 Gs nd Wtr Rltiv Prmility (Gs-tr modl) Sg Krg Pc 0.00 0.000 0.0 0.10 0.000 0.0 0.20 0.020 0.0 0.30 0.030 0.0 0.40 0.081 0.0 0.50 0.183 0.0 0.60 0.325 0.0 0.70 0.900 0.0 S Kr Pc 0.3 0.000 0.0 0.4 0.035 0.0 0.5 0.076 0.0 0.6 0.126 0.0 0.7 0.193 0.0 0.8 0.288 0.0 0.9 0.422 0.0 1.0 1.000 0.0 Oil nd Wtr Rltiv Prmility (Oil-tr modl) S Kr Kro Pco 0.27 0.000 0.900 0 0.35 0.012 0.596 0 0.40 0.032 0.438 0 0.45 0.061 0.304 0 0.50 0.099 0.195 0 0.55 0.147 0.110 0 0.60 0.204 0.049 0 0.65 0.271 0.012 0 0.70 0.347 0.000 0 38
Folloing similr procdurs usd for th nlyticl comprison, gin, to systms hving th sm rsrvoir proprtis nd thicknss r comprd (oil-tr nd gs-tr). Both systms r totlly pntrtd nd producd t th sm tr rt. Th con shp round th llor is invstigtd. Figurs 3.5 nd 3.6 sho th rsults. Irrducil tr Sturtion Irrducil tr Sturtion Spt Zon Spt Zon Gs-Wtr Oil-Wtr Figur 3.5 Numricl comprison of tr coning in oil-tr nd gs-tr systms ftr 395 dys of production. Figur 3.5 dpicts tr sturtion in th rsrvoir ftr 392 dys of production for gs-tr nd oil-tr systms. Th initil tr-hydrocron contct s t 5050 ft. In oth systms th con is dvlopd lmost in th sm shp nd hight. Figur 3.6 shos zoom vi t th top of th con for oth systms. For th oiltr systm, th con intrfc t th top is flt. For th gs-tr systm, hovr, th 39
con intrfc is con-don t th top. For this modl th totl lngth of th gs con is 1.5 ft. On cn s tht th numricl modl rprsnts xctly th sm hvior prdictd for th nlyticl modl usd prviously. Gs-Wtr Systm Oil-Wtr Systm Figur 3.6 Zoom vi round th llor to tch con shp for th numricl modl ftr 395 dys of production. From comprison of tr coning ftr rkthrough in gs-tr nd oil-tr systms, it is possil to conclud tht in gs lls, tr con is gnrtd in th sm y s in th oil-tr systm. Th shp t th top of th con, hovr, is diffrnt in oil-tr thn in gs-tr systms. For th oil-tr systm th top of th con is flt. For th gs-tr systm smll invrs gs con is gnrtd loclly round th 40
compltion. This invrs con rstricts tr inflo to th compltions. Also, th invrs gs con inhiits uprd progrss of th tr con. 3.5 Discussion Aout Wtr Coning in Oil-Wtr nd Gs-tr Systms Th physicl nlysis of tr coning in oil-tr nd gs-tr systms is th sm. In oth systms, tr coning is gnrtd hn th drdon in th vicinity of th ll is highr thn th grvittionl grdint du to th dnsity contrst tn th hydrocron nd th tr. Th dnsity diffrnc tn gs nd tr is grtr thn th dnsity diffrnc tn oil nd tr y fctor of t lst four (Muskt, 1982). Bcus of tht, th drdon ndd to gnrt coning in th gs-tr systm is t lst four-tim grtr thn th on in oil-tr systm. Prssur distriution, hovr, is mor concntrtd round th llor for gs lls tht for oil lls (gs flo qutions hv prssur squr in thm, ut oil flo qutions hv linr prssur; inrtil ffct is importnt in gs ll, nd ngligil in oil lls). This proprty mks tr coning grtr in gs lls thn in oil lls. Gs moility is highr tht tr moility. Oil moility, hovr, is lor thn tr moility. This sitution mks tr coning mor criticl in oil-tr systm thn in gs-tr systms. Gs comprssiility is highr thn oil comprssiility. Thn, gs could xpnd lrgr in th ll vicinity thn oil. Bcus of this xpnsion, gs tks ovr som xtr portion of th ll-compltion (th locl rvrs con xplind in th prvious sction) rstricting tr inflo. In short, thr r fctor incrsing nd dcrsing tr coning tndncy in oth systm. Th fct tht oil-tr systms ppr mor propitious for tr coning 41
dvlopmnt should not crt th pprnc tht th phnomn is not importnt is gstr systm. 42