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 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 3 D
Hoang The Diing Tong cdng ty Ddu khi 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 khi Md phdng md cung cdp cho cdc ky su, cdc chuyin gia thdng tin tiin lugng di phdn tich, ddnh gid vd dua ra cdc quyit dinh tdi im cho cdc hogt dgng khai thac tdi nguyen trong md. Trong bdo cdo ndy, chung tdi trinh bdy co so mo hinh vgt ly - todn trong viec xdy dung phuong trinh ddng chdy 3 pha trong 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 3 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, do vay, chung tdi hy vgng nd se dugc su dung hiiu qud trong 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 trong bd md phdng lai la he thdng phuong trinh ddng chay ciia cac pha chat luu. Bude dau tien trong 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 trong 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 trong 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 ra trong 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 trong 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, khi va nude, khae vdi chat ran, trong chat luu cac chat phan tii hda hgc hgp thanh ciia nd chuyen ddng tuong ddi vdi nhau, ndi rieng vdi chat luu ta cd hai khai niem: thanh phan chit luu-j va pha chit luu-i. Cac thanh phan chat luu-j thuc chit la cac hgp chit hda hgc, trong khi dd mdt pha chat luu-i cd the la hgp bdi nhieu thanh phin chit luu-j, mdt thanh phin chit luu-j cd thi cd mat trong mdt hoae nhieu pha chit luu-i.
Chiing ta cd nhan xet ring, md bi chan trong khdng gian ba chieu, do vay vat chit vao trong va ra khdi md deu phai cit qua bien ciia nd, cac tuong tac cd thi bien ddi khdng ddng nhit tren bien, tren thuc t l cd 2 trudng hgp sau day xay ra tren cac phin kbac nhau 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 khi 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, do rdng, do nhdt chit luu, do thim hieu dung chit luu, va cac qua trinh xay ra trong he thing md tuan theo mdt s l quy luat vat ly va cac quy luat nay dugc md ta bdi cac phuong trinh dao ham rieng.
PHUONG TRINH DONG CHAY TONG
Q U A TNghien cuu cac qua trinh vat ly va quy luat ddng chay chat luu xay ra trong 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 trong md.
Phuong trinh ddng chay cac pha chat luu trong md, ddi khi 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 trong tung phan tii cau tnic va trong toan md.
Phan tur vi phan (Cell) Moi trucmg xop
D/T tigt dien (Ay,Az)
Thanh phan chat liru-j
chay vao cell theo huongX
Pha il Pha 12
^¥L. . _ . . . iH>.
Thanh phan chat liru-j chay ra cell theo huong
X
i A x :
Hinh 1: Nguyen ly bao toan khoi luong va dong chay chat luu theo huong X Dudi gdc do md hinh toan, mien xac dinh ciia md nam trong khdng gian 3 chieu, do 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 ra khdi".
Ta ky hieu: A^ - la tdng khdi lugng nen ep ciia thanh phan chat luu-j tai thdi gian t, va tai vi tri (x, y, z) trong md (tiic khdi lugng chat luu nen lai trong da chiia trong mdt don vi thdi gian). M^ - la vector thdng lugng ciia thanh phan chat luu-j tai vi tri (x, y, z) (tiic la khdi lugng chat luu chay tren mot don vi dien tich va trong 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 3 hudng chay vao va ra khdi phan tii vi phan ciia thanh phan chat luu-j.
- Tren mdt don vi the tich Av ciia d ludi va trong mdt khoang thdi gian At, thi tdng khdi lugng thanh phin chit luu-j tich tu la:
^^•(Ai. - A „ . „ ) = Ax.Ay.Az.(A^„ -A^„,„)
856 Md hinh ddng chay 3 pha chat luu cd chuyin ddi vat c h a t ^
- Tdng khdi lugng thanh phin chat luu-j chay vao d ludi qua cac mat tiet dien d cac vi tri X, y va z trong khoang thdi gian At la:
Ay.Az.At.Mj^[^ + Ax.Az.At.Mj^i^ + Ax.Ay.At.M^^,^
- Tdng khdi lugng thanh phan chat luu-j chay ra khdi d ludi qua cac mat tiet dien d cac vi tri (x+ Ax), (y+ Ay) va (z+ Az) trong 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 nay cho Av ta cd:
At Ax Ay Az - Cho ca hai ve ciia phuong trinh tren qua gidi han tiic Ax, Ay, Az ^ 0 va
At -^ 0 ta thu dugc phuong trinh dang tdng quat ciia dong chay chat luu nhu sau:
dA: fdM.^ dM..„ dM^A J dt
J" _i j ^ + . •'^
dx 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 do (x, y, z) trong md ta cd dat mdt gieng khoan khai thac hoae bom ep thanh phan chat luu-j vdi luu lugng qj, khi 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) = 1 tai d ludi chiia dilm (x, y, z) cd dat gilng khoan khae thac, nguge lai 5(x, y, z) = 0.
Gia sir rang, ddng chay trong 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 thanh phan chit luu-j, gia su ring Cj tuong iing la phan vat chat ciia thanh phany nim trong pha i, khi dd ta cd:
X c , - l ( i = l , L ) (3)
Vi vector thdng lugng tdng cdng ciia thanh phan chat luu-j la M^ dugc xac dinh bang tdng cac vector thdng lugng thanh phin chit luu-j nam trong tat ca cac cac pha chit luu-i, nen ta cd:
M,:=tc,^M (4)
G = 1, N; M' la vector thdng lugng ciia pha chit luu-i)
Tuygn tap bao cao HQi nghj KHCN "30 nam Dau khi Vi^t Nam: Cff hpi mdi, thach thiic mdi" 857
Bang viec djnh nghia p, (kg/m^), mat do ciia pha chit luu-i, la khdi lugng ciia pha chit luu-i trong 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, khi do 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
0 day, <Dj =Pj -YjZ ; VP. = ^ x + ^ y + —i-z ; Vz = Azz; [kJ la tenxo ciia dd tham dx dy dz
hieu dung cua chat luu (mD), i^j la do nhdt ciia pha chit luu-i (mPa-s), yi = pig vdi g la gia tdc trgng trudng, Az la do cao so vdi mat bien.
Thay cac ket qua (6) vao (5) va (5) vao (4) ta thu dugc cdng thiic tinh vector thdng lugng ciia thanh phan chat luu- trong tat ca cac pha chit luu-i (Mj) nhu sau:
M, : = - Z C , ^ P , ^ ( V P , -T,VZ) = - X Q ^ P , ^ V C D , {] = l^N) (7)
Tir dinh nghia cua cac tham sd C,y, ta ciing tinh dugc luu lugng tdng cdng ciia thanh phan chat luu-j nam trong tat ca cac pha chat luu-i the cdng thiic nhu sau:
Q. = Zc,^q, (8)
Trong dd, q; la luu lugng khai thac pha chat luu-i
Tdng khdi lugng tich tu Aj ciia thanh phan chat luu-j nam trong cac pha / phu thudc vao tinh chat ciia da chiia va cac thudc tinh ciia chat luu trong md: do rdng (j) ciia da chiia, dugc dinh nghia, la phan the tich khdng gian Id hdng trong the tich da chiia, he sd bao hda 5",, dugc dinh nghia la phan tram the tich khdng gian rdng ma pha chat luu-i chiem chd, tu- dd ta cd cac cdng thiic sau:
ZS.=1 (9)
i=l
A,:=i;^#.S,=(2>tc,^p,Sj O - l ^ N ) (10)
1=1 i=i
Thay (7), (10) vao phuong trinh (2), tiic kit hgp giu luat Darcy vdi nguyen ly bao toan khdi lugng ta cd phuong trinh tdng quat md ta ddng chay nhieu pha, nhilu thanh phin chit luu nhu sau:
858 Md hinh ddng chay 3 pha ch§t luu cd chuygn ddi vat^hjt^
dt ^ZC.^p.S,
i=l "ax dz
( L
SC, 9K ^^.
( L
+ -dy
Zc,
p,k„ ao,V i = i li, dy
(11) ii, az + S(x,y,z)£c,jq,
i = l
a = i^N)
Sii dung toan tu VD, V va thay thi O- = P, - Y,Z chiing ta viit phuang trinh (11) dudi dang nit gon vdi In s l la ap suat cac pha chat luu nhu sau:
d_
at
'^ZC„P,S, 1 = i f VDfc,^p, SiL(vp, -Y,Vz)| W , y , z ) t c , q
V ,=1 J i=i V-
(12) Trong phuong trinh (12): [k] la tenso do tham tuyet ddi, kn la do tham tuong ddi cua pha chit luu-i (do tham hieu dung ciia pha chat luu kj = kkn).
Ta cd nhan xet cho phuong trinh (12) trong trudng hgp rieng vdi gia thiet md chi gdm ddng chay 1 pha, 1 thanh phan chat luu (tiic cd N = 1; L = 1; Si = 1; Cn = 1), khi dd phuong trinh (12) se cd dang don gian sau day:
_a_
at
-(^p,) = v J p , ^ ' ^ ( V P , - Y,Vz)l+6(x,y,z)q, (13)
VI: at ^ '' ap at
ap, dd - ^ + p , —
ap, ap.
Cf = - V , c, =
1 ^ " 1 J
1 d((>
a ^ at
av, _ 1 ap _
ap, " p, ap,' '' (j) ap.
dat:
suy ra:
c , = ( c , + c , ) = c.(P) => ^ ( M ) = ( M c . ) ^
at at
( ^ p , c , ) ^ = VDJp J p , B 3 k ( v p , - Y , V z ) | + 6 ( x , y , z ) q , (14) Trong (14), Ct la he sd nen ep tdng ciia nen ep da chiia (Cr) va nen ep chat luu (Cf).
PHU^ONG TRINH DONG C H A Y 3 PHA, 3 T H A N H P H A N
He gia thuyet dat ra dudi day ma ket qua dan den md hinh ciia bai toan md phdng md "Black Oil Simulator"[2]. Gia su rang, ta xet mdt md hinh ddng chay ba thanh phin hdn hgp dau, nude va khi trong ba pha chat luu dau, nude va khi ddng thdi thda man:
- Chi cd mdt thanh phan nude ton tai trong pha nude, chi cd mdt thanh phin khi tin tai trong pha khi.
- Gia sii pha diu cd thi tin tai hai thanh phin, dd la khi hoa tan va phin cdn lai khi khi dugc giai phdng hay cdn ggi la dau thd.
- Khdng cd su chuyin dii cac thanh phin vat chit trong pha nude sang pha diu, trong pha nude sang pha khi va trong pha khi sang pha nude.
Tuygn tap bao cao HQi nghj KHCN "30 nSm Phu khi Viet Nam: Cff hdi mdi, thach thuc mdi" 859^
- Chi cd su chuyin dii thanh phin vat chit mdt chilu xay ra giira pha khi sang pha diu: thanh phin khi cd thi chuyin vao va ra khdi pha dau, nhung nguge lai thanh phin diu va nude khdng bic hoi vao pha khi.
Vdi cac gia thilt tren, cac he s l Cy ciia phuong trinh (12) dugc danh gia nhu sau:
tu (a), (c) => Cwo = 0 ; C^w = 1 ; Cwg = 0
t u ( a ) , (c) = > C g o = 0 ; Cg,, = o ; Cgg = 1 (15) tu (b), (d) => Coo = mo/(mo+mg); Cow = 0; Cog = mo/(mo+mo)
Nhu vay, ta chi can phai danh gia Coo, Cog thdng qua khdi lugng mo, mg cua thanh phan dau va khi. De danh gia qua trinh chuyen ddi vat chat tu pha khi sang dau, ngudi ta da dua ra he sd hda tan cua khi trong dau, va cac tham sd dac trung cho sir thay ddi ve the tich cua cac thanh phan chat luu, cu the nhu sau:
- Ggi Rs la he sd khi hda tan trong dau trong mdt don vi the tich ciia dau d dieu kien tieu chuan.
- Ggi Vo, Vw, Vg, Vos, Vw va Vgs ian lugt la the tich ciia dau, nude, khi d dieu kien md va dieu kien tieu chuan.
- Ggi Bo, Bw va Bg lan lugt la he sd gian nd the tich ciia dau, nude va khi d dieu kien tieu chuan so vdi dieu kien md.
V, Vw v„
R = — — • VK = — ^ Ow Y ' " g V
'' ws * gs
m„ + m„ m D
= > B o = ^ ^ : ^ = > C o o = - ^ (16)
Po Pos P o ^ o
R . = ^ = ^ : - 2 ^ = ^ ^ ^ = > C o g = R s ^ (17) Vos Pgs Pos niopgs °^ ' P Q B O
Khi dd ta
V =
* OS
Pos
cd:
;Vo Bo =
= ^ c
' 0
V '
* OS
Po
Mat kbac, tir (15) ta ciing cd:
_ 1 Qgs ^ ^ _ £ g i C..= \ = - ^ ^ = > P P = ^^
^gg ' PgBg Ps B,
(^ _ 1 P w S _ v ^ ^ _ P w S / 1 OS
Cww ~ ^ ~ n u
PwBw ^" B"'^ Pw ~ R u o;
wC + C = 1 = P°^ + R Pg^ => n = ^Pg^ ^ P°^
V.00 ^ ^ o g i ^ AVS ^ P O _
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 nay ta nhan dugc:
Dau: — a
at
^ s ^
= V[:{T„(VP„-Y„Vz)} + Q„ (19)
860 Md hinh ddng chay 3 pha ch5t luu cd chuyen ddi vat chat.
Nuoc: — c
at B . ; :V^TJVP„-Y.Vz)} + Q, (20)
Khi: o
'dt B^ B„
) = V 4 T ^ ( V P ^ - Y , V Z ) ) + V : ^ R J „ ( V P „ - Y „ V Z ) } + ( Q ^ + R , Q „ ) (21)
Tir (9), ta cung cd: So + Sg + S , = 1 (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 nay 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) (23)
Pcgo ^ Pg - Po (ap suat mao dan he thdng khi - dau) (24) Tham s l Tj (i = o, w, g) tuong ung dugc ggi la he sd truyen dan thanh cac phan
chit luu dau, nude va khi theo cac hudng trong khdng gian, dugc xac dinh nhu sau:
kk„„ k k .
(i=o,w,g) (25)
T = - vdi T. kk. ny
^i,B,
Tir (8) => Q„
^i.B,
-5(x,y,z)
T = ' '^ h B
1 P B
r o c
l o ' Qv
^i.B,
6(x,y,z) 1 P B
r w V
Qg=5(x,y,z)-^q^ (26) Nhu vay, he phuong trinh (19) - (24) neu tren la phuong trinh ddng chay 3 pha, 3 thanh phan chat luu dau, nude va khi, chiing ta cd 6 phuang trinh vdi 6 an sd la Pj, Sj (i = o, w, g), do vay ve phuong dien ly thuyet bai toan cd ldi giai.
Neu trong gia thuyet ciia md hinh 3 pha dau, nude va khi khdng cd mat ciia pha khi, khi dd ta cd bai toan 2 pha dau va nude, phuong trinh (21) va (24) se bi loai bd, phuong trinh (22) trd thanh: So + S , = 1, va ket qua trong trudng hgp nay se cd he 4 phuong trinh vdi 4 an sd Pj, Sj (i = o, w).
Trong thuc te, he thdng phuang trinh ddng chay 3 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 trong cac bd phan mem md phdng ciia cac cdng ty dau tren the gidi. Ve nguyen tac, chiing ta cd the giai bai toan nay true tiep ma khdng can thuc hien bat ky mdt bien ddi nao khae tren co sd mdt luge dd sai phan an Crank- Nicholson ddi vdi ca 6 phuong trinh neu tren, tuy nhien trong trudng hgp nay 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 = 1 - So - Sw ; Pv, = Po - Pcwo; Pg = PQ + Pcgo, ta de dang kilm tra dugc he thing (19) - 24) se giam xulng cdn he 3 phuong trinh vdi 3 In s l
l a PQ, OQ, O,,..
Tuygn tap bao cao HQi nghj KHCN "30 n2m Dau khi 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 4 + V L { G , P „ } + VG{(^„p„+^^p^+X^pJgVz}
+ 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)
(27)
C.= ^ s, aB„ , s„ aB^ ^ Sg aB^ B^S, aR ^
^B„ ap„ B^ ap„
(tdng nen ep)
B, 5P„ B„ ap o y
Q.=BoQo+B^Q„+BgQg=5(x,y,z) ^ + iw. + .-^8 (tdng luu lugng khai thac)
vqG,p„} =
' Z T . ^ . B . , T
^ " ax
V i = o
r u
5R, ''°' dx
vi=o az
H.
r
ae ap
w cw<
dx dx aOg ap„.
+T.
5R, ''"' dz
"^ ay ay aB„ ap
5 ^ dx ap„
i^''t--
V,=o
aR, ''"' dy
ap„
ay az
+ T ae ap
w cwc
az az
^^ dx dx ^' dy dy
ae ap ^
ego , TT g c g c
'' dz dz + + „ ae ae^
T Y — ^ + T Y ——
oz ' 0 ^. WZ ' W -\
az az
ae^ 5R
+ T Y — ^ - B T Y
g z ' g - u , g o z ' az az Az
Trong phuong trinh (27), cac 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, khi 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 nay. Ndi rieng khi tinh ap suat cua pha khi, chiing ta can kiem tra dieu kien tdn tai pha khi 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 trong phuang phap sai phan biiu ban trong 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 3 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 trong md hinh, dieu nay giiip cho hg danh gia va dieu chinh cac tham s l diu vao mdt each hgp ly khi 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 trong cac gia thuyet vat ly dua ra 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 thanh cdng.
Vdi su phat trien to ldn ciia chuyen nganh toan iing dung va cua cdng nghe thdng tin, phuong trinh ddng chay 3 pha chat luu (27) hien nay cd nhieu phuong phap ky thuat sd kbac nhau de giai, van de quan trgng nhat dugc dat ra la: lira chgn phuong phap sd de giai va danh gia tinh hieu qua ciia phuong phap nay xet tren tat ca cac phuong dien nhu tinh dn dinh ciia thuat toan, tdc do hdi tu, thdi gian tinh toan, bd nhd va kha nang td chiic lap trinh.
TAI LIEU THAM KHAO
1. Henry B. Criclow. Modem reservoir engineering: A simulation approach. Prentice Hall Inc.
2. G. W. Thomas, 1981. Principles of hydrocarbon reservoir simulation. Internal Human Resources Development Coporation.
3. William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling.
Numerical recipes. Cambridge University Press (Fortran version).