Mô hình dòng chảy 3 pha chất lưu có chuyển đổi vật chất giữa các pha trong môi trường xốp 3D

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