ABSTRACT. Keyword: Capillary pressure curve; relative permeability; tight sandstone; water trapping ABSTRAK

Transcription

1 ain Malayiana 46()(7): The Appliation of Fatal Dienion on Capillay eue Cuve to Evaluate the Tight andtone (Aplikai Dieni Faktal ke ata Lengkung Tekanan apilai untuk Menilai Batu ai adat) Chunhua Guo, Yu Yang*, ing Yan, Ruili Zhou & Xiaodong eng ABTRACT The ok of ga tight eevoi i oe heteogeneou than that of onventional andtone eevoi and i oe pone to wate-blokage beaue of the invaion of opeation fluid. Thi pape peented a new appoah fo the analyi of the apillay peue uve fo tight ga eevoi. Heein, the atuation equation with fatal dienion poved the peviou obevation that the log-log plot of apillay peue againt wate atuation i a taight line, whih i quite diffeent fo the popula obevation by Coey oelation. How to tanfo the apillay peue uve to elative peeability uve wa alo diued with fatal dienion. The fatal dienion of apillay peue, whih i not only an indiation of heteogeneity, an alo eveal the potential wate blok in tight ga well. If the ok ha highe fatal dienion, being at the ae wate atuation, the apillay peue will be highe and the elative peeability of wate will be alle, whih ean highe injetion peue i equied to diplae the tapped wate in eevoi. It i uggeted that fo the tight ga pay zone with highe fatal dienion, oe peaution hould be taken to pevent the wate tapping duing dilling o tiulating opeation. eywod: Capillay peue uve; elative peeability; tight andtone; wate tapping ABTRA Batuan di takungan kedap ga lebih heteogen daipada takungan batu pai konvenional dan lebih endeung kepada penahanan ai keana peneobohan daipada eai opeai. eta ini engeukakan pendekatan bau untuk analii lengkung tekanan kapilai takungan kedap ga. Oleh itu peaaan penepuan dengan dieni faktal ebuktikan peehatian yang lepa bahawa plot log-log tekanan kapilai tehadap ai penepuan adalah gai luu dan agak bebeza daipada peehatian popula oleh ekali Coey. Bagaiana engubah lengkung tekanan kapilai untuk keteluan bandingan lengkung juga dibinangkan dengan dieni faktal. Dieni faktal tekanan kapilai bukan hanya ebagai petunjuk konta, juga boleh endedahkan poteni blok ai dala telaga ga yang padat. Jika batuan epunyai dieni faktal yang tinggi pada penepuan ai yang aa, tekanan kapilai akan enjadi tinggi dan ketetelapan elatif ai akan enjadi keil yang beakud tekanan panutan yang tinggi dipelukan untuk enggantikan ai yang tepeangkap dala takungan. Adalah diaankan aga zon kaka kedap ga dengan dieni faktal yang lebih tinggi eelukan lebih banyak langkah keelaatan untuk enegah ai daipada tepeangkap eaa penggeudian atau opeai peangang. ata kuni: Batu pai padat; ketetelapan elatif; lengkung tekanan kapilai; peangkap ai Intodution It ha been aepted by eevoi enginee that the heteogeneity of tight ga i oe eiou than onventional ga eevoi. How to haateize the iotutue of tight ga with the appopiate appoah ha been hallenging fo a long tie. When tudying the apillay peue uve of tight ga, Well and Aaefule (985) found that the popula odel of Book and Coey (966) goe well with the andtone with peeability geate than oday, but it ay not be appliable in tight ga. Lekia and Evan (988) obeved that log-log plot of apillay peue againt wate atuation, intead of noalized wate atuation, i a taight line. With the intodution of fatal theoy by Mandelbot (98), oe and oe eeahe tied to utilize it to tudy the fatal natue of eevoi ok and othe poou edia. It i eaonable to deontate the obevation of Lekia and Evan (988) with fatal theoy. Due to the oplex poe tutue, the elative peeability uve of tight ga eevoi i tie-onuing to eaue by the onventional table o tanient tate ethod uitable fo onventional eevoi and it i of geat ue to apply apillay peue uve to opute the elative peeability uve.

2 64 Aqueou phae tapping epeent a ignifiant eaon fo ipaied podutivity in any ga eevoi. Bennion et al. (994) have alo povided a detailed diuion of the ehani of aqueou phae tapping. enny et al. (983) pointed out that the apillay peue, wettability and elative peeability ae ontolling the load wate eovey following hydauli fatuing teatent (Wang 7). ine the fatal dienion ha etain link with both of the apillay peue and elative peeability, it an be ued to evaluate the potential wate bloking in tight ga eevoi. THE CAILLARY REURE MODEL FOR TIGHT ROC Book and Coey (966) ade a lage nube of obevation on onolidated ok oe and onluded that the apillay peue veu noalized wettingphae atuation ould be expeed with the following * elation, * / λ = C ( ). () Noalized wetting-phae atuation * i defined a: * wi =, () wi whee λ i the poe ize ditibution index; and C i a ontant. A indiated by (), the againt * hould be plotted a a taight line on log-log plot. lg = lg C lg(*) / λ. (3) Howeve, Well and Aaefule (985) found that the odel fo Book and Coey (966) goe well with the andtone with peeability geate than ioday and ay not be appliable in tight ga. Lekia and Evan (988) alo obeved that the Coey appoah fo the deteination of the lope of veu * i not appliable to tight ga and. Baed on the data fo Noth-weten Coloado, Eat Texa and Albeta and Canada, they found that the againt wetting phae atuation on log-log plot i taight line. ine both of the obevation of Coey and Lekia wee fo the lab tet, why hould thee be the quite diffeent onluion? We an ake a judgeent fo the apillay peue odel with fatal dienion. In the 98, Fenh atheatiian Mandelbot (98) founded the new diipline of Fatal Geoety, whih peent a iple but effetive way to explain vaiou oplex natual phenoena. The atix poe yte in ok i fatal in evey ene. Aoding to fatal theoy, the fatal dienion of poe ufae i given by a A l D, (4 whee A i the aea of poe ufae; l i the length ale; D i the fatal dienion of poe ufae, the value a of whih i between and. Yang et al. (5) expeed the elation between the volue and adiu of poe a; V 3 D. (5) V i the volue of poe whoe adiu i. D i the fatal dienion of poe volue, whoe value i between and 3. Diffeentiating equation 5 give: dv d D. (6) The uulative volue of poe whoe adii ae geate than i expeed a: D ( > ) = = ( ) V a d b. (7) The total volue of onneted poe i V t expeed a: t D ( in ). (8) in V = a d = b The peentage of the uulative poe volue whoe adii ae lage than i expeed a. 3 ( > ) V D = = Vt in. (9) Beaue of the fat that in i uh alle than, (9) an be iplified a: =. () In the ealie tage of euy injetion, the euy i injeted into the lage poe. Duing the injetion of euy, beaue the uulative volue of euy injeted i the uulative volue of poe whoe adii ae lage than. i alo the atuation of non-wetting phae. The Laplae equation i: σ oθ =. () ubtituting () into equation (), the elationhip between and the atuation of non-wetting phae i: = in D 3 The atuation of wetting phae = = in. () D 3 i defined a:. (3)

3 65 Taking the logaith of equation 3 on both ide yield: ubtituting the (3) into equation (7) and (8), the elative peeability ae expeed a lg = ( D 3)(lg lg ) (4) in The in i the enty apillay peue. It i uggeted fo (4) that the againt wetting phae atuation on log-log plot i taight line, whih onfi the onluion of Lekia and Evan (988). To explain the diffeent obevation of Lekia and Coey, let have a eview of the oe ued by the. The obevation fo Book and Coey ae baed on aple with highe peeability, whoe ieduible wetting-phae atuation wi ae uh alle than thoe of the tight aple Zhen and Gao (7). That i to ay, beaue the diffeene between * and an be negligible fo ok with all wi, the Coey equation i eaonable fo onventional ga pay zone with highe peeability. Howeve, in the ae of tight ga aple, the value of wi annot be ovelooked, the obevation fo Lekia i oe eaonable. It hould be teed that the (4) i a geneal funtion between and wetting phae atuation, whih an be ued fo all kind of peeable ok, epeially the tight ga eevoi. The elative peeability odel In 949, uell eoended a ethod to alulate the elative peeability fo the apillay peue uve. w nw = = '. (5). (6) But the u of and w by uell ethod, i at nw any atuation, whih doe not oinide with the onluion of the laboatoy expeient that w + nw <. Lekia and Evan (988) alo found a odel fo tight ga and, it ha been ued uefully in the tudy of tight ga eevoi. The ga and wate elative peeability odel given by Lekia and Evan i: w = d. (7) 5 D 3D = =. (9) w 5 D = ( ) ( ). () g Taking the logaith of (9) on both ide yield: 3D lg( w) = lg( ). () 3 D If we do not have elative peeability uve, we an opute the fatal dienion D fo apillay uve with (4) and the elative peeability uve an be oputed with (9) and (). The heteogeneity of tight ok aple with fatal He and Hua (998) alulated the poe ize ditibution of oe fo oil eevoi and found that the fatal dienion epeent the extent of heteogeneity haiiah and Muhaad yuki (5). To deontate the elationhip between heteogeneity and fatal, the geotatitial oeffiient deibing the heteogeneity of poe an be edefined with fatal dienion. The ean value of poe adii i defined a: = d. () ubtituting () to () and eaanging it a: D 3 d = = 4. (3) D The oting oeffiient of poe adii i defined a δ: ( ) δ = d. (4) ubtituting () and (3) into (4) give: D 3 3 D D 3 D 3 D 3 D d 4 D 5 D 4 D δ = =. (5) The oeffiient of vaiation C v an alo be given a: g = ( ) d d '. (8) δ (4 D) / Cv = = [ ]. (6) (3 D)(5 D)

4 66 TABLE. The geotati paaete veu fatal dienion D ( µ ) δ ( µ ) Cv FIGURE. Relative peeability of wate veu wate atuation Heein the fatal dienion i deived fo the apillay peue, whih i the fatal dienion of poe ditibution. Angulo and Otiz (99) found that the fatal dienion of poe volue ale i in the ange. to.9. ohn (988) ade a eie of eaueent on andtone, hale and abonate and found that the fatal dienion of and tone i between.7 and.89. The fatal dienion of hale and abonate ae alo with the ae ange. Table i oputed with the apillay uve fo tight and tone aple of eng Laizhen Goup in ihuan Bain. It i hown in Table that if the fatal dienion ineae, the oeffiient of vaiation and the oting oeffiient will ineae aodingly. Thi pove that the fat that fatal dienion an indiate the heteogeneity of poe ditibution. edit the potential of wate tapping in tight ga eevoi The fatal dienion D an alo be taken a a key paaete to evaluate the potential of wate phae tapped in tight ga eevoi. The elative peeability of wate i expeed a (9). The hape of the wate elative peeability indiate the potential of wate tapping. It an be een fo Figue that the onave uve how a ignifiant deeae of elative wate peeability with a all deeae of the wate atuation. If the fatal dienion D i.7, when the wate atuation deeae fo to.8, the elative peeability of wate will deeae fo to.. Howeve, if the fatal dienion D i., when the wate atuation deeae fo to.8, the elative peeability of wate will deeae fo to.3. It i een fo Figue that thee i a lowe elative peeability in the ok with highe D opaed with that with alle D at the ae wate atuation, whih indiate that the tapped wate will be uh oe diffiult to be diplaed by ga. Conluion The apillay peue odel heein ha deontated the obevation of Lekia on tight ga that the apillay peue againt the wate atuation in log-log plot i taight line. The odel uggeted by Coey that the apillay peue againt the noalized wate atuation in log-log plot ould be taken a a taight line i uitable fo the ok with highe peeability, and annot be ued with tight pay zone. The fatal dienion an help to ealize the onveion fo the euy-injetion peue to elative peeability uve, whih i tie onuing to eaue by onventional expeiental tet fo tight ok aple. The fatal dienion, whih i poved to be indiation of heteogeneity, alo indiate the potential wate bloking. If the ga pay zone ha highe fatal dienion, the elative peeability of wate will be alle at ae wate atuation. When dilling o tiulating the ga pay zone with highe fatal dienion, oe eaue hould be taken in advane to pevent the wate bloking.

5 67 REFERENCE Angulo, R. & Otiz, N. 99. Fatal Dienion fo Meuy Intuion Capillay Tet. Caaa, Venezuela: oiety of etoleu Enginee, Mah 8-. Bennion, D.B., Bietz, R.F., Thoa, F.B. & Ciolai, M Redution in the podutivity of oil and low peeability ga eevoi due to aqueou phae tapping. Jounal of Canadian etoleu Tehnology 33(9): ETOC Book, R.H. & Coey, A.T opetie of poou ateial affeting fluid flow. Jounal of Injetion and Dainage Diviion, oeeding of ACE 9, No. IR: 6. He, C.Z. & Hua, M.Q Fatal geoety deiption of eevoi poe tutue. Oil & Ga Geology 9(): 5-3. haiiah Haji Badi & Muhaad yuki Ngah. 5. A ini ale bath eato fo the podution of pal baed polyol. ain Malayiana 44(6): ohn, C.E Fatal eaueent of andtone, hale and abonate. Geophy. Re. 93(4): Lekia,.D.L. & Evan, R.D Chaateization of Natually Fatued Lentiula Tight Ga and Reevoi - A Reevoi iulation Appoah. Univeity of Okalahoa hool of etoleu and Geologial Engineeing Reeah Repot, Noan, Okla. Mandelbot, B.B. 98. The Fatal Geoety of Natue. an Fanio: Feean. pp enny, G.., Conway, M.W. & Bioe, J.E Enhaned Load Reovey Tehnique Ipove tiulation Reult. E pape 49 peented at the 983 Annual Tehnial Confeene and Exhibition, an Fanio, Ot. E-49-M. uell, W.R Capillay peue-thei eaueent uing euy and the alulation of peeability the efo. Tan AIMME 86: Wang, J.D., Zeng, Y.J., Xu, Y.J. & Feng,.Q. 7. Analyi of the influene of tunnel potal etion ontution on lope tability. Geology, Eology, and Landape (): Well, J.D. & Aaefule, J.O Capillay eue and eeability Relationhip in Tight Ga and. ape E/DOE 3879, oeeding of the 985 E/ DOE Joint ypoiu on Low eeability Ga Reevoi, Denve, Colo, May 9-. Yang, Y., He, C.Z. & Lin, F. 5. Coent on Reply to oent on Analytial deivation of Book-Coey type apillay peue odel uing fatal geoety and evaluation of ok heteogeneity. Jounal of etoleu iene and Engineeing 33: Zhen,. & Gao, W.M. 7. Geologial touit oute planning of Henan povine baed on geologial eli zoning. Geology, Eology, and Landape (): Chunhua Guo College of Envionent and Civil Engineeing Chengdu Univeity of Tehnology Chengdu 659 Yu Yang* & ing Yan tate ey Laboatoy of Oil and Ga Reevoi Geology and Exploitation Chengdu Univeity of Tehnology Chengdu 659 Ruili Zhou eto-engineeing Reeah Intitute of Noth Oil and Ga Banh inope, Zhengzhou 456 Xiaodong eng Reeah Intitute of Zhanjiang Banh CNOOC Enegy Tehnology & evie Co. Zhanjiang 5457 *Coeponding autho; eail: yangyu@dut.n Reeived: 6 Januay 7 Aepted: June 7