A Revision Article of Oil Wells Performance Methods

Transcription

1 A Revisin Aticle Oil Wells emnce Methds The ductivity inde well, dented y, is mesue the ility the well t duce. It is given y: Whee: Welle ductivity inde, STB/dy/sig Avege (sttic) esevi essue, sig Welle stilized il lw te, STB/dy Welle stilized ttm-hle lwing essue, sig The ductivity inde is genelly mesued duing ductin test n the well, whee the well is shut-in until the sttic esevi essue is eched. The well is then llwed t lw t cnstnt lw te nd stilized ttm-hle lwing essue. It is imtnt t nte tht the ductivity inde is vlid mesue nly i the well is lwing t seud-stedy stte cnditins. Theee, in de t ccutely mesue the ductivity inde well, it is essentil tht the well is llwed t lw t cnstnt te suicient munt time t ech the seud-stedy stte cnditin. A lt the ttm hle essue,, vesus the il lw te,, n il well is clled the Inlw emnce Reltinshi nd is eeed t s IR. The IR cuve is cnstucted eithe the esent esevi essue the utue esevi essue. The esent IR cuve well cn e geneted vi mny methds. The methds e gued int tw min ctegies: The ist ctegy, tht uses esevi metes, includes the integl nd Fetkvitch methds. The secnd ctegy includes set Vgel-tye emiicl celtins. T cnstuct the IR cuve well using well emnce, em the llwing stes: Use the sttic esevi essue nd the stilized welle te nd essue ( & ) t clculte s llws: Cnstuct the IR cuve y ssuming vius vlues cesnding s llws: ( ) nd clculting the

2 I. The Integl Fm Dcy s equtin cn e eessed mthemticlly s: kh e 4. ln 0.75 s w k µ B d The IR cuve is cnstucted y ssuming vius vlues nd clculting the cesnding. T cnstuct the IR cuve well using well emnce lng with the integl methd, em the llwing stes: Use the sttic esevi essue nd the stilized welle te nd essue t clculte s llws: µ B d Cnstuct the IR cuve y ssuming vius vlues cesnding s llws: nd clculting the µ B d II. Fetkvitch Methd Fetkvitch (97) stted with Dcy s equtin: He cnsideed tw cses: kh e 4. ln 0.75 s w k µ B d

3 w e s B kh 0.75 ln 4. µ 0.75 ln 4. w e s B kh µ 0.75 ln 4. w e C s B kh µ. Stuted Oil Resevi When the esevi essue nd the ttm-hle lwing essue e th elw the ule-int essue, the il lw te cn e witten s: The cnstnt C is eeed t s the emnce ceicient. The IR cuve is cnstucted y ssuming vius vlues nd clculting the cesnding using the ve equtin.. Undestuted Oil Resevi > Tw cses e cnsideed: Cse : Cse : III. Cnstnt ductivity Inde Methd The IR cuve well cn e geneted using the cnstnt ductivity inde ch. The ductivity inde well is deined s mesue the well t duce. It is given y:

4 Whee: ductivity inde, STB/dy/si Oil lw te, STB/dy Vlumetic vege dinge e essue (sttic essue), si Bttm hle lwing essue, si The ductivity inde is genelly mesued duing ductin test n the well. The well is shut-in until the sttic esevi essue is eched. The well is then llwed t lw t cnstnt lw te nd stilized ttm-hle lwing essue. It is imtnt t nte tht the ductivity inde is vlid mesue nly i the well is lwing t seud-stedy stte cnditins. Theee, in de t ccutely mesue the ductivity inde well, it is essentil tht the well is llwed t lw t cnstnt te suicient munt time t ech the seud-stedy stte cnditin. The methd is summized s llws: Use the stilized welle te nd essue ( & ) t clculte s llws: Cnstuct the IR cuve y ssuming vius vlues nd clculting the cesnding s llws: IV. Vgel Methd ( ) Vgel (968) used cmute gm t genete the IRs sevel hytheticl stuted il esevis ducing unde wide nge cnditins. When lying his methd, the nly dt equied e: the vege esevi essue, the il ule-int essue, nd the stilized welle te nd essue ( & ). Vgel s methdlgy cn e used t edict the IR cuve the llwing tw tyes esevis:. Stuted Oil Resevis Use the stilized welle te nd essue & t clculte ( ) m s llws: ( ) m

5 5 Cnstuct the IR cuve y ssuming vius vlues nd clculting the cesnding s llws: m Undestuted Oil Resevis > Use the stilized welle te nd essue & t clculte the ductivity inde s llws: Clculte the il lw te t the ule-int essue: Cnstuct the IR cuve y ssuming vius vlues nd clculting the cesnding s llws: V. Wiggins (99) Methd Wiggins (99) used u sets eltive emeility nd luid ety dt s the sic inut cmute gm t genete the IRs sevel hytheticl stuted il esevis ducing unde wide nge cnditins. The nly dt equied e: the vege

6 esevi essue, the il ule-int essue, nd the stilized welle te nd essue ( & ). This methd is cnsideed the llwing tw tyes esevis:. Stuted Oil Resevis Use the stilized welle te nd essue & t clculte ( ) m s llws: ( ) m Cnstuct the IR cuve y ssuming vius vlues cesnding s llws: nd clculting the ( ) m 48. Undestuted Oil Resevis > Use the stilized welle te nd essue ( & ) t clculte the ductivity inde s llws: ( ) ( ) Clculte the il lw te t the ule-int essue: ( ) Cnstuct the IR cuve y ssuming vius vlues nd clculting the cesnding s llws: 6

7 VI. Wiggins (996) Methd In 996, Wiggins deived n equtin the edictin il well emnce. His equtin cn e used s llws:. Stuted Oil Resevis Use the stilized welle te nd essue & t clculte m s llws: 4 m Cnstuct the IR cuve y ssuming vius vlues nd clculting the cesnding s llws: 4 m Undestuted Oil Resevis > Use the stilized welle te nd essue & t clculte the ductivity inde s llws: Clculte the il lw te t the ule-int essue:

8 ( ) Cnstuct the IR cuve y ssuming vius vlues nd clculting the cesnding s llws: ( ) VII. The Klins-Clk Methd Klins nd Clk (99) sed n inlw eessin simil in m t tht Vgel s nd cn e used t estimte utue IR dt. This methd is cnsideed the llwing tw tyes esevis:. Stuted Oil Resevis Use the stilized welle te nd essue & t clculte ( ) m s llws: Whee: ( ) m d (.4 0. ) d Cnstuct the IR cuve y ssuming vius vlues cesnding s llws: nd clculting the ( ) m d. Undestuted Oil Resevis > Use the stilized welle te nd essue & t clculte the ductivity inde s llws: 8

9 9 d Clculte the il lw te t the ule-int essue: Cnstuct the IR cuve y ssuming vius vlues nd clculting the cesnding s llws: d VIII. F s Methd The F slutin methd is given y: 0 y Using the lest sque methd, we tin system thee equtins in thee unknwns 0,, : y y y is the nume dt ints. In mti m, this cn e witten s:

10 0 y y y 0 4 The we is slved t minimize the esidul t men sque (RRMS): i z s z cl RRMS Once the set equtins hs een slved, the llwing equtins e slved: 0 m,,m,m y This methdlgy cn e used t edict the IR cuve the llwing tw tyes esevis:. Stuted Oil Resevis Cnstuct the IR cuve y ssuming vius vlues nd clculting the cesnding s llws: m,. Undestuted Oil Resevis > Use the stilized welle te nd essue & t clculte the ductivity inde s llws:

11 .8 Clculte the il lw te t the ule-int essue: Cnstuct the IR cuve y ssuming vius vlues nd clculting the cesnding s llws:.8

12 edicting Futue IRs As the vege esevi essue declines, the IR cuve is shited. Thee e sevel methds tht e designed t ddess the lem hw the IR might shit. Fu simle imtin methds e esented.. Vgel s Methd Vgel s methd vides ugh imtin the utue ( ) m, t the seciied utue, s llws: ( ) ( ) 0. 0., 8 m, m,, Whee the suscits nd ee t the utue nd evius esectively. The clculted m, cn e used t edict the utue IR t,. ( ),,. Fetkvitch This methd, sed y Fetkvitch (97), vides simle imtin the utue m, t the seciied utue, s llws: ( ) ( ) ( ) m, m,,, Whee the suscits nd ee t utue nd esent esectively. The clculted ( ) m, cn e used t edict the utue IR t. Wiggins Methd,. Wiggins (99) sed the llwing eltinshi: ( ) ( ) , 84 m, m,,,, 4. Stnding s Methd Stnding (970) etended the lictin Vgel s t edict utue IR well s unctin esevi essue. He nted tht Vgel s equtin cn e nged s:

13 ( ) m 0.8 () Stnding intduced the ductivity inde s llws: ( ) 0. 8 He then deined the esent (cuent) ze dwdwn ductivity inde s: m () ( ) m.8 () Whee inde y: is Stnding s ze-dwdwn ductivity inde. The is elted t the ductivity 0.8 (4).8 ) m Cmining equtins () nd () t eliminte ( yields: ( ) ( ) (5) Whee the suscits ees t utue cnditin. Stnding suggested tht the esent vlue y the llwing eessin: is estimted m k ub (6) k ub I eltive emeility dt is nt ville, ( ) ( ) cn e estimted m: (7) Stnding s methdlgy edicting utue IR is summized in the llwing stes: Use the stilized welle te nd essue & t clculte ( ) m s llws:

14 4 0.8 m Clculte using: m.8 Clculte using: B u k B u k i eltive emeility dt is nt ville, cn e estimted m: Cnstuct the IR cuve y ssuming vius vlues nd clculting the cesnding s llws: