694 Phat trign phuong phap du bao phan bo lu ong nu 6c bom ep t6l uu su dung phan mem tinh via^^ PHAT TRIEN PHlTONG PHAP DlT BAO PHAN BO LU O^fG NlTOC BO>M EP TOI UtJ StT DUNG PHAN M E M TINH VIA VA T[.]
Trang 1PHAT T R I E N PHlTONG P H A P DlT B A O P H A N B O LU O^fG NlTOC BO>M EP TOI UtJ StT D U N G P H A N M E M TINH VIA V A T H U A T T O A N
P H A N T I C H H O I Q U Y
Nguyen Thi Dire Duong Ngoc Hai
Viin Co hpc
N57(52)
TOM T A T
Mdt phuong phdp du bdo phdn bd lugng nu&c trong cdc giing bom ep tdi mi de gidm tinh trgng ngap nu&c trong cdc giing khai thac vd tdng hi sd thu hdi ddu dugc trinh bdy Trong phucmg phdp ndy, mdt thudt todn tdi uu dugc goi Id phdn tich hdi quy dugc sir dung kit hgp v&i phdn mim tinh via Phuong phdp da dugc dp dung thu nghiim cho mdt bdi todn don gidn hod lien quan din viec xdc dinh phdn bd lugng nu&c bom ip hgp ly cho
md Bgch Hd Cdc kit qud nhdn dugc da cho thdy hiiu qud ciia phuong phdp
GIOI THIEU
Cho den nay, Bach H6 van la m6 dau e6 san lugng dau th6 Ion nhat Viet Nam Sau mot qua trinh khai thac dai, de duy tri ap suat via, c6ng nghe bom ep nuoc da duge ap dung tai mo Dong trong via chiu anh huong true tiep ciia luu lugng d6ng trong cac gieng khai thae va bom ep Vi vay, viee xac dinh mot phan b6 luu lugng dong trong eae gieng la can thiet de tang he s6 thu h6i dau va giam lugng nuoc trong san pham
Ngay nay cae phan b6 luu lugng hgp ly trong cac gieng chii yeu duge xac dinh bang m6 phbng s6: dau tien, can thiet phai lira chon mot phan mem tinh via thich hgp va thiet
ke m6 hinh via M6 ta via sir dung trong m6 hinh dugc thiet ke va kiem dinh tren co so cae dtr lieu khai thac va bom ep lich sir Mot khi sir tuong hgp vai dtr lieu lich su nhan dugc, m6 hinh eo the duge sir dung de du bao hoat dong tuong lai ciia mo [1]
Tuy nhien ngay ca voi mot m6 hinh thich hgp va vai mot bo dtr lieu via tin cay xac dinh phan b6 luu lugng hgp ly trong cac gieng bom ep va khai thac van la mot nhiem vu rat phire tap va tieu t6n rat nhieu thai gian Vi du, voi mot m6 co hon 100 gieng nhu m6 Bach H6, neu luu lugng eiia m6i gieng ehi thay d6i trong 2 gia tri, s6 phuong an phan b6 luu lugng khae nhau se la Ion hon 2'°°(> 10'^'') De m6 ph6ng het s6 phuong an phan b6 nay can den hang tv' nam Vi vay, can thiet phai ap dung nhiing ky thuat phan tich va thuat toan phii hgp de day nhanh qua trinh tim kiem phuong an phan b6 hgp ly
Bai bao trinh bay mot thuat toan co kha nang giai quyet mot s6 bai toan t6i uu trong qua trinh tim kiem phan b l luu lugng hgp ly trong cac gieng bom ep eiing nhu trong cac
gieng khai thac Thuat toan dc xuit dua tren ky thuat phan tieh h6i quy thuong d\xgc sir
dung trong phuc h6i lich su tu dong va giai mot s6 bai toan t6i uu khae ([3 4]) Nhu mot
\i du minh hoa ap dung ciia phuong phap cho mot bai toan t6i uu boa phan b6 nuoc bom
ep cho mo Bach H6 dk lugng diu liy ra la Ion nhit duge trinh bay ngan gon
Trang 2Tuygn tap bao cao Hoi nghj KHCN "30 nam Phu khi Viet Nam: Co' hoi moi, thach thiic moi" 695
CO SO CUA C A c P H A N M E M TINH VIA
Cae phin mim tinh via da dugc phat trien manh va sir dung rong rai tren the gioi: IMEX-Canada, Eclipse-USA, Athos-French, v.v ([5, 7]) Cae phan mem nay dugc xay dimg dua tren nin tang viec giai d6ng nhieu pha/nhieu thanh phan trong m6i truong r6ng (vai cac mo hinh mot do ring, hai do r6ng, v.v ) De don gian, duoi day ehiing t6i se chi m6 ta ngan gon truang hgp m6 hinh ba pha mot do r6ng:
He phuong trinh m6 ta dong nhan dugc bang each thay the luat Darcy vao cac phuong trinh bao toan vat chat pha:
V
V
[kK
u B
(Vp„-p,,gVD)
rvp.-p.gVD;
(Vp^-p^gVD)
-<l,-Rs^o =
d_
dt
d
(1)
(2)
+ V
d
(yp.,-9„gyD)
dt ^
(3)
Nhung moi lien he bo sung can dugc cung cap de dong kin m6 hinh toan hoc Vi du
de don gian, trong truong hgp dang nhiet, se bao g6m:
Dac tinh ciia m6i truong r6ng: cj) = ^{p^);
Cac dac tinh d6ng - dit da: p^ = ;?„ + p^^^,{S„,Sj, p^=p„+ /?,.„„,(5„,5 J ,
^g-'^~'^o~^w^ kri = k^i(S^,,S^)
Va cac dac tinh d6ng: B, = B, (p„), fi = |i(p„), p = p(p„)
Dieu kien ban dau va cac dieu kien bien can de lam day dii va giai m6 hinh toan hoc
Do CO the la phan b6 ap suat va do bao hoa pha a moi diem luoi tai thai diem ban dau (/ = 0) Tuy nhien, co the t6ng quat hon, ap suat pha dugc cho tai mot do sau quy chieu (D = 0) va doi vai cac diem kh6ng gian kbac, m6i lien he mat do va ap suat mao dan dugc sir dung de tinh toan ap suat va do bao hoa qua phuong trinh vi phan:
dPi
dD ^Pi(Pi)g
Tai cac bien ngoai cua via, cac dieu kien bien dugc sir dung duoi dang lai:
-X^ = h(p-pJ + q,
dn
Tai cac gieng khai thac va bom ep, luu lugng dong dugc xac dinh nhu sau:
q'^WlY Mlh ^(P-P )
rin(r^/rJ-3/4 + Six'B'^ " ^^ ^''
Trang 3Phuong phap IMPES dugc sir dung va he phuong trinh dai sl thu dugc co thi dugc giai boi cac phuang phap ADI, SOR, SIP, v.v , trong d6 phuong phap SIP la phi biin ban
CO SO TOAN H O C CUA THUAT TOAN PHAN TICH HOI QUY
M6 ph6ng de cai thien phan b6 luu lugng trong cac gieng c6 the dan toi viec tim loi giai cua bai toan t6i uu sau day trong kh6ng gian nhieu chieu:
T6i thieu ham muc tieu:
Q = Q{X) : XeQcR"
Trong do:
Q la ty le nuoc/dau (WOR - ty le nuoc tren dau thu dugc tir cac gieng khai thac)
X = {X^,X2,•••,xJ' eQczR"; X^ la luu lugng cua gieng thu j (luu lugng nuoc
vai cac gieng bom ep hoae luu lugng dong vai cac gieng khai thac)
Q xac dinh tir cac dieu kien lien quan den kha nang thiet bi va muc dich dat ra cua qua trinh khai thae
Q{X) duge xac dinh boi phan mem tinh via
Cac phuong phap phan tich h6i quy da chimg t6 tinh hieu qua trong nhieu ITnh vue khoa hoc tren the gioi Mgt s6 ky thuat thuoc nhom nay da dugc ap dung thanh c6ng trong viec phuc h6i lich sir tu dong cho cac m6 hinh tinh via Trong cac phuong phap phan tich
h6i quy, cac dao ham ciia ham muc tieu img voi cac tham s6 Xj kbac nhau duge phan tich d6ng thai de xac dinh su thay d6i ciia cac tham s6 do de ham muc tieu Q gan hon vai
mot gia tri t6i thieu [8] Dang phuong phap phan tich h6i quy th6ng dung nhat la eae phuong phap do d6e Co so toan hoc cua cac phuong phap nay co the dugc m6 ta nhu sau: Tat ca cac phuong phap do d6c deu bat dau tir mot bo gia tri uoc doan cho moi tham
s6, XJ, ma bo cac gia tri nay co the viet t6 hgp duoi dang mot vecto:
r=[x:,xi ,x:)'
Gia tri ciia ham muc tieu Q tsx X* la Q[X' ) Bo gia tri tham sl X khae dugc chon sao cho:
X = X' +/^ = [x*+l:a„X\ +AX2, ,X; +AY„y'
va mot gia tri mai ciia ham muc tieu Q(X) nhan dugc. N I U Q(X) < Q[X'), sir thay
d6i cac tham s6 tir X' toi X se lam Q gan hon voi cue tiiu Cac phuong phap do die tim kiem each sir dung t6c do thay dii cua Q voi cac z\X kbac nhau dk lira ebon mot AA' dac trung ma no se lam Q huong ve gia tri tii thilu ciia no Noi chung, cac phuong phap do d6c sir dung t6c do thay doi cua Q trong lan can ciia X' dk chgn chieu va/hoac do Ion tii
uu cho AX Nguyen ly ciia chiing co thi duge mo ta ngin gon nhu sau ([9, 10]):
Gia sir rang ham muc tieu Q la duong, no e6 the dugc viet duoi dang:
Q = R'(X„X„X„ ,XJ
Trang 4Tuygn tap bao cao Hoi nghj KHCN "30 nam Phu khi Viet Nam: Co' hoi moi, thach thiic moi" 697
Dl Q dat cue tiiu tai X' +AX, phuang trinh sau cin dugc thoa man:
dQ = 2R(X + A X ) — ^ - - ^ = 0 ( , \dR{x'+Ax) ^ vai i = \,2, ,n
dX, ' ' dX,
Mgt khai triln Taylor quanh diem X* chi bao g6m dao ham bae nhat eho bieu thire:
R{r ^NXV RirVy^NX,^-^
Thay the vao nhan dieu kien dat cue tieu, ta nhan dugc:
dR[X*-rNX\ ^ ^-
—^ / = 0 voi z = l,2, ,^ dX
^^^,dR[r+^x)_d_R^
ex dx,
Sap xep lai se cho ta: > NX,=-R\X voi /=l,2, ,n
j:{dx,dx^ ' ^ 'dx,
trong do tat ea cac dao ham dugc tinh tai X*
Bieu thuc tren c6 dang: AiOC = B
Trong do:
PR dR
dX dX,
A, J = ^^^ , \<i<n , \<j<n
va
B,=-Rir)^ , \<l<n
^ 'dx,
Cac dao ham bae nhat thu dugc bang each xao tron tham so X, mot lan trong khi giir
nguyen cac bien khae kh6ng thay d6i va tinh toan tac dong len R Phuong trinh co the
dugc giai cho AX boi bat ky phuang phap giai nao AX dugc sir dung de chi ra chieu
thay d6i cua X Cac buoc dugc m6 ta chi tiet hon trong [2]
• • •
Nam 2000, Vien Co hoc da thuc hien mot nhiem vu nghien cim voi su tai trg va
cong tac ciia XNLD Vietsovpetro nham muc dich tim mot s6 phan b6 t6t hon cho luu
lugng bom ep va khai thac trong cac gieng, de tang he s6 thu h6i dau va giam chi phi san
xuit trong tuong lai
Nhiem vu nghien cim dugc thuc hien mgt phin bing mo phong s l hoat dong cua via:
Phin mim tinh via IMEX cua CMG (Computer Modeling Group-Canada) dugc sir
dung trong nghien cuu nay [5] Dac trung ciia phin mim nay la m6 ph6ng diu den,
mo hinh dong ba pha trong cac via khi, khi - nuoc, diu - nuoc va diu - nuoc - khi
Trang 5D I xir ly clu true dirt gay kh6ng d6ng nhat phirc tap eua via m6 Bach H6 m6 hinh
"gia hai do ring"' [2] dugc sir dung
- Cae du lieu vl tinh chit eua dat da va d6ng trong via duge XNLD Vietsovpetro cung elp Thu tue phue hoi lich sir dugc thuc hien cho toi thoi dilm ngay 1/9/2000 T6ng sl gilng duge sir dung trong khoang thai gian du bao la 142, bao g6m 113 gilng khai thae va 29 gieng bom ep
- Tinh toan du bao duge thue hien cho khoang thai gian tir ngay 1/9/2000 toi ngay 31/12/2020 Dilu kien ap dat cho hoat dong khai thac trong tirong lai la t6ng the tich nuoc bom ep bing ting the tieh dong khai thae (trong dieu kien via)
Ttr phuang an phan b l luu lugng bom ep tai thai diem bat dau m6 ph6ng du bao (goi la phuang an phan b l 2000), bin phuang an phan b6 moi Al, A2, A3 va A4 da dugc xay dung bai thay dii luu lugng eua tit ea cae gieng ciing mot ty le Su khae nhau ve t6ng luu lugng bom ep giija eae phuong an nay voi phuang an 2000 dugc cho trong Bang 1 Cac phuong an phan b l nay dugc sir dung nhu cac truang hgp co so trong phep phan tieh h6i quy
Bang 1: Su- thay doi cua tong lu-u luo-ng bom ep cua cac phuo-ng an phan bo luu luoTig
A1,A2, A3, A4
Phuang dn phdn bd
Al A2 A3 A4
Thay ddi ciia tdng luu lugng bam ep (so v&l phuang dn phdn bd 2000)
+ 10%
+20%
-10%
-20%
B6n phuong an phan b6 mai Cl, C2, C3 va C4 da nhan dugc bai ap dung thuat toan
phan tich h6i quy de xuat 0 day, cac phuong an phan b6 A l , A2, A3 and A4 dugc
su-dung nhu nhiJng phan b6 uoc doan ban dau eho cac phuong an phan b l Cl, C2, C3 va C4 tuong img Ket qua m6 phong du bao sir dung cac phuong an phan b l khae nhau dugc t6ng ket trong Bang 2
Bang 2: Cac chi so khai thac co- ban trong tinh toan dy bao hoat dong cua mo Bach Ho
voi cac phu-oTig an phan bo bom ep khae nhau
Phuong dn
phdn bd
DP2000
Al
A2
A3
A4
Cl
C2
C3
C4
Tdng nu&c bam ip (triiu tdn)
384,5 398,1 407.6 381,4 369,9 386.1 404,8 366,7 345,3
Tdng sdn lugng ddu khai thde (triiu tdn)
161,05 160,80 161,30 159,05 157,81 163,42 165,28 162,58 162,12
He sd thu hdi ddu
(%)
36,03 35,97 36,08 35,58 35,30 36,56 36,97 36,37 36,3
Do ngap nu&c sdn phdm
(%)
2010
78,92 80,79 80,45 79,47 77,66 78,00 77,68 74,94 70,72
2020
81.86 82,52 82,52 80,81 81,25 83,95 86,38 84.33 84.57
Trang 6Tuygn tap bao cao Hoi nghj KHCN "30 nam Dau khi Viet Nam: Co- hoi moi, thach thiic mdi" 699
Nhu th6ng thuang, hai tieu chuin chinh dugc sir dung dl danh gia cac phuong an phan b l la:
- He s l thu hii diu/ Ting san lugng dau khai thac
- Hieu qua diy diu eua viec bom ep nu6c/D6 ngap nuoc san pham
So sanh cac phuong an phan b6 cho thay:
- Su khae nhau ve he s6 thu h6i dau gitra cac phuong an phan b6 luu lugng bom ep
la kh6ng Ion lam Sir khae nhau Ion nhat ve he s6 thu h6i dau la 1,67%) (gitra phuong an C2 va phuang an A4) Cae phuong an phan b6 eo he s6 thu h6i dau Ion hon phuong an phan b6 2000 la Cl, C2, C3, C4 va A2
- Trong khi do, sir khae nhau ve hieu qua bom ep nuoc la kha lan Cac phuang an phan b6 C l , C2, C3 va C4 deu dat hieu qua bom ep nuoc t6t ban nhieu so voi phuong an phan b6 2000 Hieu qua bom ep nuoc ciia cac phuang an con lai ( A l , A2, A3 va A4) la tuong tu vai phuong an phan b6
2000 Duong dac trung day dau ciia cac phuang an C l , C2, C3 va C4 dugc thay tren cac Hinh 1 den 4 cimg voi duong cong day dau ciia phuang an
2000 va s6 lieu do dac
Co the thay dugc ro rang la cac phuong an phan b6 thu nhan duoc bang phuong
phap phan tich h6i quy n6i tren la t6t hon nhieu so vai cac phuong an phan b6 con lai Nhting thir nghiem phuong phap nay da cho thay rang thuat toan de ap dung va da thanh
c6ng trong viec thu nh6 ham muc tieu quan tam Q la tong luu lugng nuoc trong cac gieng
khai thac
jS
o
D
90
80
70
60
50
40
30
20
10
0]
^
j-•
- P A C l
- PA Co so 2000 Thucte
0.1
/ i
yy
/ /
/ r
/ J
/ r / /
/ / / /
if
11
11
J J
//
T^ ^^r\ 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0.15 0.2 0.25 0.3
He so thu hoi, p.cLv
^^^^
\ :
0.35
, ,
0 4
Hinh 1: Cac duong dac trung dSy diu (PhuoTig an phan bo Cl, 2000 va do dac)
Trang 790
80
70
60
50
40
30
20
10
n 1
-•
- PAC2
- PA Co so 2000
•rhucte
0.1
/ J
/ d / /
//
//
/ / / / / / '
//
1 i ^ r i 1 1 1 1 1 J 1 J 1 1 1 1 1 1
0.15 0.2 0.25 0.3
He so thu hoi, p.d.v
^N' ^
, 1 , , 0.35 ' ' 0.4
t X j X
Hinh 2: C^c dirong dac tnmg day dau (Phuong an phan bo C2,2000 va do dac)
o
a
90
80
70
60
50
40
30
20
10
Ol
T
I
-•
- PAC3
- PACoso2000 Thucte
0.1
/ J
/ J
/ / / /
/ f
/ 1
/ y
1 p
1 /
/ / / / / /
0.15 "0.2 0.25 0.3
He so thu hoi, p.dv
j ^ ^ ^
1 1 1 1
0.35
, ,
0.4
Hinh 3: Cac ducmg dac trung day dau (Phuong an phan bo C3, 2000 va do dac)
Trang 8Tuygn tap b^o cao HQI nghj KHCN "30 nam D^u khi Viet Nam: Co- hoi moi, thach thiic moi" 70]
o
Q
90
80
70
60
50
40
30
20
10
n 1
~
;
•
- PAC4
- PACoso2000 Thucte
0.1
/ ' / / / / / / /
/ W
/ /
/ / / / / /
0.15 0.2 0.25 0.3
He so thu hoi, p.dv
1 1 1 1
0,35
, , 1 0.4
Hinh 4: Cac duong dac tru-ng day dau (Phuo'ng an phan bo C4, 2000 va do dac) KET LUAN
Ket qua ap dung thir nghiem cho m6 Bach H6 cho thay thuat toan phan tieh h6i quy
de xuat la rat htru ich trong viec tim kiem phan b6 luu lugng bom ep va khai thac hgp ly trong cac gieng Cac phuang an phan b6 nhan dugc bang phep phan tich h6i quy deu t6t hon cac phuong an phan b6 khae, dac biet ve hieu qua day dau ciia nuoc bom ep
GIAI THICH KY HIEU
/ = Chi s6 pha; w, o, g: nuoc, dau,
va khi tuong iing;
5,: He so the tich via, mV m^;
C,: He s6 nen, 1/Pa;
D: Do sau, m;
g: Trong luc, m^/s;
\k\: Ten xo tham, mD;
A:„ : Do tham tuong dii;
/: Lop da;
p^: Ap suat Pa;
p^: Ap suat diem sui bot, Pa;
p^ ,^,: Ap suat mao dan dau/khi Pa;
Pcm '• Ap suat mao dan nuoc/khi Pa;
q^: Luu lugng, m /s;
r^: Ban kinh ngoai cua cua gieng, m;
r^ : Ban kinh day gieng, m;
5, : Do bao hoa pha;
t : Thai gian, s;
|i,: Do nhoi;, cp;
p,: Mat do, kg/m^;
(|): Do r6ng;
WI: Chi s6 gieng;
Trang 9TAI LIEU THAM KHAO
1 Mattax C C , Dalton R.L., 1990 Reservoir simulation Society of Petroleum Engineers
Inc, USA
2 Duong N.H et al, 2001 Examination of influences of oil producing rate on recovery
efficiency of White Tiger field based on numerical reservoir simulator Report of
research project of Institute of Mechanics & Vietsovpetro Joint Venture, Hanoi, (2001)
{in Russian)
3 Lapidus L., 1967 Optimal control of engineering processes Blaisdell Publishing Co.,
Waltham, MA
4 Bui T.T., Tran V.T., 1998 Optimization methods Transportations Pub., Hanoi {in
Vietnamese)
5 Computer Modeling Group, 1998 IMEX - Advanced oil/gas reservoir simulator:
Version 98 user's guide Canada, 593 p
6 Nigmatulin R.L, Duong Ngoc Hai, Fedorov K.M., 1991 Mechanics, Heat and mass
transfer in saturated porous media: Application into petroleum technology In: Convective Heat and Mass Transfer in Porous Media, NATO ASI Series E 196,
KluwerPub Co., p 9 3 9 - 9 6 1
7 Duong Ngoc Hai, Dang The Ba, 2002 Numerical model of phase
three-dimensional flow in porous media for reservoir simulation J Mechanics, NTSC of Vietnam, Vol 24, No 3
8 Hoffman J., 1993 Numerical methods for engineers and scientists McGraw-Hill Inc.,
NewYork
9 Jahns H.O., 1966 A rapid method for obtaining a two-dimensional reservoir
description from well pressure response data SPEJ, Dec 1966, p 315 - 27
10 Thomas L.K., et al, 1972 A nonlinear automatic history matching technique for
reservoir similation models SPEJ, Dec 1972, p 508 - 14