854 Md hinh ddng chay 3 pha chat luu cd chuygn ddi vat chat^ M O H I N H D O N G C H A Y 3 P H A C H A T LlTU C O C H U Y E N D O I VAT C H A T G I L T A C A C P H A T R O N G M O I TRlTONG X O P 3D H[.]
854 Md hinh ddng chay pha chat luu cd chuygn ddi vat chat^ M O H I N H D O N G C H A Y P H A C H A T LlTU C O C H U Y E N D O I V A T C H A T G I L T A C A C P H A T R O N G M O I T R l T O N G X O P 3D Hoang The Diing Tong cdng ty Ddu Viit Nam TOM T A T Md phdng md la mdt ITnh vuc ung dung cua todn hgc bao gdm cdc khdi niem, cdc ky thudt vi md hinh vdt ly - todn vd tap hgp cdc phuong phdp gidi sd di phdn tich md ddu vd Md phdng md cung cdp cho cdc ky su, cdc chuyin gia thdng tin tiin lugng di phdn tich, ddnh gid vd dua cdc quyit dinh tdi im cho cdc hogt dgng khai thac tdi nguyen md Trong bdo cdo ndy, chung tdi trinh bdy co so mo hinh vgt ly - todn viec xdy dung phuong trinh ddng chdy pha mdi truong xdp cd su chuyin ddi vdt chdt giua cdc pha, vd sau day cdn nhdc t&i mdt dgng phuo'ng trinh dugc biin ddi tu hi phuo'ng trinh pha niu tren, phuong trinh ndy thudc logi phuong trinh dgo hdm riing logi Parabol, v&i mdt dn sd la dp sudt pha ddu, vay, chung tdi hy vgng nd se dugc su dung hiiu qud tinh todn vd lap trinh CAC QUAN SAT CHUNG VE HE THONG M O Md hinh vat ly - toan cho bai toan md phdng md cd the bieu thi nhu mdt he thdng hop den [1], ma trgng tam ciia nd la bd md phdng, ndi dung chinh bd md phdng lai la he thdng phuong trinh ddng chay ciia cac pha chat luu Bude dau tien nghien ciiu md phdng la quan sat md tren tat ca cac khia canh: ve cau tnic khdng gian, cac qua trinh vat ly, cac thudc tinh vat chat md, cac muc tieu ciia cdng tac md phdng, v.v Ve cau triic khdng gian, md la mgt khdi lap the vat chat nam dia cau dugc gidi ban bdi cac mat bien xac dinh, md cd hinh dang ndn, cau tnic md bao gdm nhieu ldp dia chat, ngoai md cd the tdn tai he thdng dut gay chia cat cac ldp dia chat lam cho cac ldp dia chat bien ddi khdng lien tuc theo vi tri khdng gian Vat chat md la cac thuc the tu nhien tdn tai d hai dang chat ran (da chiia) va chat luu Chat luu cd the cd nhieu loai nhu dau, va nude, khae vdi chat ran, chat luu cac chat phan tii hda hgc hgp ciia nd chuyen ddng tuong ddi vdi nhau, ndi rieng vdi chat luu ta cd hai khai niem: phan chit luu-j va pha chit luu-i Cac phan chat luu-j thuc chit la cac hgp chit hda hgc, dd mdt pha chat luu-i cd the la hgp bdi nhieu phin chit luu-j, mdt phin chit luu-j cd thi cd mat mdt hoae nhieu pha chit luu-i Chiing ta cd nhan xet ring, md bi chan khdng gian ba chieu, vay vat chit vao va khdi md deu phai cit qua bien ciia nd, cac tuong tac cd thi bien ddi khdng ddng nhit tren bien, tren thuc tl cd trudng hgp sau day xay tren cac phin kbac cua bien: khdng cd thdng lugng chit luu tren bien, cd thdng lugng chat luu di qua bien Tuygn tap bao c^o H^i nghj KHCN "30 n2m DSu Viet Nam: Cff hdi mdi, thach thuc mdi" 855 Tai thdi gian ban diu, ta cd mdt he cac dilu kien ban dau cho tit ca cac tham sd nhu ap suit chit luu, rdng, nhdt chit luu, thim hieu dung chit luu, va cac qua trinh xay he thing md tuan theo mdt sl quy luat vat ly va cac quy luat dugc md ta bdi cac phuong trinh dao ham rieng PHUONG TRINH DONG CHAY TONG Q U A T Nghien cuu cac qua trinh vat ly va quy luat ddng chay chat luu xay mdt phan tii "vi phan" cua md, sii dung ly thuyet "tien tdi gidi ban" ciia toan hgc ngudi ta nhan dugc he thdng cac phuong trinh dao ham rieng ma nd md ta ddng chay md Phuong trinh ddng chay cac pha chat luu md, ddi cdn ggi la phuong trinh lien tuc, dugc xay dung dua tren co sd ciia cac nguyen ly can bang vat chat, nguyen ly bao toan khdi lugng, bao toan ddng lugng (dinh luat Darcy) va nguyen ly chuyen ddi vat chat giiia cac pha chat luu tung phan tii cau tnic va toan md Phan tur vi phan (Cell) D/T tigt dien (Ay,Az) Moi trucmg xop Thanh phan chat liru-j chay vao cell theo huongX Pha il Pha 12 ^¥L _ iH> Thanh phan chat liru-j chay cell theo huong X i Ax: Hinh 1: Nguyen ly bao toan khoi luong va dong chay chat luu theo huong X Dudi gdc md hinh toan, mien xac dinh ciia md nam khdng gian chieu, vay khdi hop chii nhat dugc chgn lam d ludi (phan tu vi phan) vdi kich thudc vi phan tuong ling la Ax, Ay, Az (Hinh 1), nguyen ly can bang vat chat dugc phat bieu nhu sau: ''Ddi V&i mdi d lu&l, thdnh phdn chdt luu-j tich tu se bdng hiiu sd giira thdnh phdn chdt luu-j chdy vdo v&i thdnh phdn chdt luu-j di khdi" Ta ky hieu: A^ - la tdng khdi lugng nen ep ciia phan chat luu-j tai thdi gian t, va tai vi tri (x, y, z) md (tiic khdi lugng chat luu nen lai da chiia mdt don vi thdi gian) M^ - la vector thdng lugng ciia phan chat luu-j tai vi tri (x, y, z) (tiic la khdi lugng chat luu chay tren mot don vi dien tich va mdt don vi thdi gian) Khi dd, qua trinh xay dung phuong trinh ddng chay tdng quat dua tren nguyen ly bao toan khdi lugng dugc thuc hien theo trinh tu cac bude sau day: - Xac dinh hudng chay vao va khdi phan tii vi phan ciia phan chat luu-j - Tren mdt don vi the tich Av ciia d ludi va mdt khoang thdi gian At, thi tdng khdi lugng phin chit luu-j tich tu la: ^^•(Ai - A „ „ ) = Ax.Ay.Az.(A^„ -A^„,„) 856 Md hinh ddng chay pha chat luu cd chuyin ddi vat c h a t ^ - Tdng khdi lugng phin chat luu-j chay vao d ludi qua cac mat tiet dien d cac vi tri X, y va z khoang thdi gian At la: Ay.Az.At.Mj^[^ + Ax.Az.At.Mj^i^ + Ax.Ay.At.M^^,^ - Tdng khdi lugng phan chat luu-j chay khdi d ludi qua cac mat tiet dien d cac vi tri (x+ Ax), (y+ Ay) va (z+ Az) mdt khoang thdi gian At la: Ay.Az.At.Mj,„,,, + Ax.Az.At.Mjy,y,^y +Ax.Ay.At.Mj^,^,^, - Thiet lap phuong trinh can bang ve khdi lugng tren co sd cac ket qua tinh toan, chia ca hai ve ciia phuang trinh cho Av ta cd: At - Ax Ay Az Cho ca hai ve ciia phuong trinh tren qua gidi han tiic Ax, Ay, Az ^ va At -^ ta thu dugc phuong trinh dang tdng quat ciia dong chay chat luu nhu sau: dA:J dt fdM.^J" dx _i dM „ dM^A j^+ •'^ dy dz = -V[Mp, Mj=Mj,x + Mj^y + Mj,z a = l , N ) (1) Trong cdng thiic (1), VD la ky hieu toan tii tuong duong vdi Divergence (Div) Gia sii rang, tai mdt vi tri cd tga (x, y, z) md ta cd dat mdt gieng khoan khai thac hoae bom ep phan chat luu-j vdi luu lugng qj, dd phan tii vi phan cd chiia diem (x, y, z) cd sir mat mat hoae bd sung nang lugng, nhu vay phuong trinh (1) dugc viet lai vdi dang day dii nhu sau: - ^ = -V[M^±6(x,y,z)Q^ a = l , N ) (2) dt d day, ham sd 5(x, y, z) la ham Dirac, 5(x, y, z) = tai d ludi chiia dilm (x, y, z) cd dat gilng khoan khae thac, nguge lai 5(x, y, z) = Gia sir rang, ddng chay md cd L pha chat luu vdi chi sd quy udc la / (z = 1, L), mdi pha chat luu-i cd su pha trdn ciia N phan chit luu-j, gia su ring Cj tuong iing la phan vat chat ciia phany nim pha i, dd ta cd: Xc,-l(i=l,L) (3) Vi vector thdng lugng tdng cdng ciia phan chat luu-j la M^ dugc xac dinh bang tdng cac vector thdng lugng phin chit luu-j nam tat ca cac cac pha chit luu-i, nen ta cd: M,:=tc,^M G = 1, N; M' la vector thdng lugng ciia pha chit luu-i) (4) Tuygn tap bao cao HQi nghj KHCN "30 nam Dau Vi^t Nam: Cff hpi mdi, thach thiic mdi" 857 Bang viec djnh nghia p, (kg/m^), mat ciia pha chit luu-i, la khdi lugng ciia pha chit luu-i phin lo hdng ciia mdt don vi the tich da chiia, ta suy ra: M'=PiV, (5) (/ = 1, L; v_ la vector van tdc pha chat luu-i) Gia su rang cac dieu kien md thda man mdt sd gia thuyet vat ly de cd the ap dung dinh luat Darcy, vector van tdc v' cua mdi pha chat luu-i cd mdi quan he vdi gradient (V) ciia ap suat chat luu-i (P,) va dugc xac dinh bdi cdng thiic sau: V, =-M(VP,-Y,Vz) = - ^ V O , (6) (i=l,L) 5P 5P 5P day, Coo=-^ Pos (16) Po^o R = ^ = ^ : - ^ =^^^=>Cog = R s ^ Vos Pgs Pos niopgs °^ 'PQBO (17) Mat kbac, tir (15) ta ciing cd: C = _ (^ Qgs \ = - ^ ^ ^gg ' _ PgBg PwS ^ ^ => _v^ _£gi ^^ PP= Ps ^ B, _ PwS / OS Cww ~ ^ ~PwBw n u "'^^"Pw ~BRw C + C = = P°^ + R Pg^ V.00 ^ ^ o g i ^ AVS u o; => n = ^ PO ^Pg^ ^ P°^ _ PoBo PoB„ B„ Thay cac ket qua danh gia cho Cy tu cac cdng thiic (15) - (17) vao (12), va thay cac danh gia cua Pg, p„ tir (18) vao (12), gian udc he sd p^^, p.^^ ^^ Pws ^ hai ve ciia mdi phuong trinh ta nhan dugc: Dau: a — at ^ s ^ = V[:{T„(VP„-Y„Vz)} + Q„ (19) Md hinh ddng chay pha ch5t luu cd chuyen ddi vat chat 860 Nuoc: c — (20) :V^TJVP„-Y.Vz)} + Q, B.; at Khi: o ) = V4T^(VP^-Y,VZ)) + V:^RJ„(VP„-Y„VZ)} + ( Q ^ + R , Q „ ) B^ 'dt (21) B„ Tir (9), ta cung cd: So + Sg + S, = (22) Giiia hai pha chit luu khdng pha trdn dugc tdn tai hien tugng mao dan, ap suat mao din {P,) la ap suit tin tai doc theo mat tilp xiic giGa hai pha chat luu va dugc tinh nhu la hieu sl giiia ap suit pha khdng dinh udt vdi ap suat pha dinh udt ( Pg = Pn - Pnw)Vay, Pcwo = Po - Pw (ap suit mao dan he thdng dau - nude) Pcgo ^ Pg - Po (ap suat mao dan he thdng - dau) (23) (24) Tham s l Tj (i = o, w, g) tuong ung dugc ggi la he sd truyen dan cac phan chit luu dau, nude va theo cac hudng khdng gian, dugc xac dinh nhu sau: T=- ^i,B, vdi T kk„„ kk T = ny ^i.B, ' '^ h B Tir (8) => Q„ -5(x,y,z) P B r o c lo ' kk ^i.B, Qv 6(x,y,z) (i=o,w,g) (25) Qg=5(x,y,z)-^q^ (26) P B r w V Nhu vay, he phuong trinh (19) - (24) neu tren la phuong trinh ddng chay pha, phan chat luu dau, nude va khi, chiing ta cd phuang trinh vdi an sd la Pj, Sj (i = o, w, g), vay ve phuong dien ly thuyet bai toan cd ldi giai Neu gia thuyet ciia md hinh pha dau, nude va khdng cd mat ciia pha khi, dd ta cd bai toan pha dau va nude, phuong trinh (21) va (24) se bi loai bd, phuong trinh (22) trd thanh: So + S, = 1, va ket qua trudng hgp se cd he phuong trinh vdi an sd Pj, Sj (i = o, w) Trong thuc te, he thdng phuang trinh ddng chay pha (19) - (24) dugc giai bing cac phuong phap sd nhu sai phan hiiu ban hoae phan tii hiiu ban Hien nay, phuong phap sai phan hiiu ban dugc iing dung nhieu nhat cac bd phan mem md phdng ciia cac cdng ty dau tren the gidi Ve nguyen tac, chiing ta cd the giai bai toan true tiep ma khdng can thuc hien bat ky mdt bien ddi nao khae tren co sd mdt luge dd sai phan an CrankNicholson ddi vdi ca phuong trinh neu tren, nhien trudng hgp ta nhan dugc mdt he thdng phuong trinh sai phan vdi sd rang bugc khdng Id, day la ban chi ciia phuong phap De giai quyet cac ban che tren, ngudi ta tiep tuc bien ddi he (19) - (24) theo xu hudng giam sd bien, dua ve sd lugng phuang trinh it hon Chang ban, bang phep thay thi cac dai lugng P^, P,, va S^ nhu sau: Sg = - So - Sw ; Pv, = Po - Pcwo; Pg = PQ + Pcgo, ta de dang kilm tra dugc he thing (19) - 24) se giam xulng cdn he phuong trinh vdi In sl l a PQ, OQ, O,, Tuygn tap bao cao HQi nghj KHCN "30 n2m Dau Viet Nam: Cff hdi mdi, thach thuc mdi^ 861 Mat kbac, bang mdt day cac phep biin dii co ban nhu thay bien, liy dao ham, nhdm cac hang thiic, v.v tu he (19) - (24) tac gia da thu dugc mdt phuong trinh dao ham rieng loai Parabol vdi mdt In sd la ap suit pha diu {Po), phuong trinh dugc viit nhu sau: ( t ) C , ^ = V D ( ( ^ „ + ^ „ + ^ J V P + V L { G , P „ } + VG{(^„p„+^^p^+X^pJgVz} (27) + VC(XgVP,^o}-VC(^wVPc.o} + H,+Q, Trong dd: ^o=B„T„; X^=B^\', ?^g=BgTg (he sd dich chuyen ciia cac pha dau, nude va khi) ^ s, aB„ , s„ aB^ ^ Sg aB^ C.= ^B„ ap„ B^ ap„ aR ^ B^S, B, 5P„ B„ apo y (tdng nen ep) Q.=BoQo+B^Q„+BgQg=5(x,y,z) ^ + iw + -^8 (tdng luu lugng khai thac) vqG,p„} = ' Z T ^ B , T 5R, ^ ''°' dx ^ " ax Vi=o r u vi=o w cw< dx dx r aOg ap„ ^^ dx dx + „ i^''t dx V,=o 5R, ap„ ''"' dz az az ae ap H aR, ap„ ''"' dy ay +T "^ ay ay w az aB„ ap cwc az ae ap ^ ego ^' dy dy ae ae ap +T , TT g cgc '' dz dz ae^ ae^ T Y — ^ + T Y —— + T Y — ^ - B T Y oz ' ^ WZ ' W -\ gz'g az -u, g oz' + 5R Az az Trong phuongaztrinh (27),azcac hang thiic Q„ H, bao gdm cac he sd gian nd the tich, cac dai lugng PVT va luu lugng khai thac cua cac pha dau, va nude Giai phuang trinh (27) bang phuang phap sai phan hiiu ban, thi du nhu, phuong phap ADI (Alternating Direction Method), tir cac gia tri ban dau ciia tat ca cac tham sd (tai n = 0), tiic tii bude thdi gian (t = n), ta se tinh dugc ap suat pha dau Po tai bude thdi gian (t = n + 1) tai cac diem giiia cac d ludi, biet gia tri Po ta se tinh dugc tat ca cac an sd cdn lai nhu P,„ Pg va S, (i = o, w, g) tai bude thdi gian (t = n + 1) tren co sd thay thi P^ vao he (19) - (24) va kilm tra cac dieu kien can bang ciia he phuong trinh Ndi rieng tinh ap suat cua pha khi, chiing ta can kiem tra dieu kien tdn tai pha tren co sd kilm tra gia tri ap suit bao hda Tir ket qua tren, chiing tdi hy vong ring, nlu sii dung cac ky thuat mdi phuang phap sai phan biiu ban nhiing nam gin day, thi viec giai phuong trinh (27) se don gian hon so vdi viec true tilp giai he thing (19) - (24) 862 Md hinh ddng chay pha chat luu cd chuvgn ddi vat chat»^ K E T LUAN Viec tim hieu sau sac md hinh bai toan ddng chay nhieu pha chat luu tir co so xay dung md hinh vat ly - toan cd y nghia quan trgng cho cac ky su, qua dd hg se nam chac y nghia vat ly cac tham sd md hinh, dieu giiip cho hg danh gia va dieu chinh cac tham sl diu vao mdt each hgp ly khai thac va su dung cac he thing phan mem md phdng md Ndi rieng, de nghien ciiu, phat trien va xay dung mdt bd phin mem md phdng md thi tinh diing dan cac gia thuyet vat ly dua cho viec thiet lap phuong trinh ddng chay cac pha chat luu, md hinh ve dieu kien bien ddi vdi mdt md cu the, van de xii ly sd lieu de danh gia cac tham sd dau vao cho he thdng la cac yeu td quan trgng va cd y nghia quyet dinh den cdng Vdi su phat trien to ldn ciia chuyen nganh toan iing dung va cua cdng nghe thdng tin, phuong trinh ddng chay pha chat luu (27) hien cd nhieu phuong phap ky thuat sd kbac de giai, van de quan trgng nhat dugc dat la: lira chgn phuong phap sd de giai va danh gia tinh hieu qua ciia phuong phap xet tren tat ca cac phuong dien nhu tinh dn dinh ciia thuat toan, tdc hdi tu, thdi gian tinh toan, bd nhd va kha nang td chiic lap trinh TAI LIEU THAM KHAO Henry B Criclow Modem reservoir engineering: A simulation approach Prentice Hall Inc G W Thomas, 1981 Principles of hydrocarbon reservoir simulation Internal Human Resources Development Coporation William H Press, Brian P Flannery, Saul A Teukolsky, William T Vetterling Numerical recipes Cambridge University Press (Fortran version) ... chat giiia cac pha chat luu tung phan tii cau tnic va toan md Phan tur vi phan (Cell) D/T tigt dien (Ay,Az) Moi trucmg xop Thanh phan chat liru-j chay vao cell theo huongX Pha il Pha 12 ^¥L _... chay md cd L pha chat luu vdi chi sd quy udc la / (z = 1, L), mdi pha chat luu-i cd su pha trdn ciia N phan chit luu-j, gia su ring Cj tuong iing la phan vat chat ciia phany nim pha i, dd ta... thd - Khdng cd su chuyin dii cac phin vat chit pha nude sang pha diu, pha nude sang pha va pha sang pha nude Tuygn tap bao cao HQi nghj KHCN "30 nSm Phu Viet Nam: Cff hdi mdi, thach thuc mdi"