1、%隐式求解方法%t 为投产后某一时刻，单位：天%d:迭代时间；%Pwf1:W1 井底流压;%Q2:W2 井产油量 ;function P,d,Pwf1,Q2=implict(t)%油藏参数Pini=20;u=5e-3;C=2e-4;Q1=30;Pwf2=15;dx=200;dy=200;dt=24;n=t*24/dt;%迭代时间步数re=0.208*dx;rw=0.1;%渗透率K=0 259 222 200 190 180 185 0 0 0 0;259 259 222 200 190 180 185 185 0 0 0;310 310 240 235 228 210 195 195 0 0
2、0;330 330 290 270 250 230 205 197.5 180 185 0;350 350 300 280 259 222 200 190 180 185 185;340 340 320 290 310 240 235 228 210 195 195;355 355 335 315 310 290 270 250 230 205 205;0 0 0 0 325 300 280 240 210 215 215;0 0 0 0 340 320 290 260 235 225 225;0 0 0 0 355 335 315 295 275 255 0;%厚度H=K/50; %孔隙度F
3、ai=(K.*0.02+15)/100;%地层压力P=Pini*ones(10,11);%P(1,:)=0;%P(2:10,1)=0;%P(2:10,11)=0;%P(2:4,8:10)=0;%P(8:10,2:4)=0;%系数矩阵%初始化a=zeros(10,11);b=zeros(10,11);c=zeros(10,11);d=zeros(10,11);e=zeros(10,11);%for i=2:9for j=2:10a(i,j)=3600e-9*dt*2*H(i,j-1)*K(i,j-1)*K(i,j)/u/C/Fai(i,j)/dx/dx/(H(i,j-1)*K(i,j-1)+H(
4、i,j)*K(i,j);b(i,j)=3600e-9*dt*2*H(i,j+1)*K(i,j+1)*K(i,j)/u/C/Fai(i,j)/dx/dx/(H(i,j+1)*K(i,j+1)+H(i,j)*K(i,j);c(i,j)=3600e-9*dt*2*H(i+1,j)*K(i+1,j)*K(i,j)/u/C/Fai(i,j)/dx/dx/(H(i+1,j)*K(i+1,j)+H(i,j)*K(i,j);d(i,j)=3600e-9*dt*2*H(i-1,j)*K(i-1,j)*K(i,j)/u/C/Fai(i,j)/dx/dx/(H(i-1,j)*K(i-1,j)+H(i,j)*K(i,
5、j);e(i,j)=-1-a(i,j)-b(i,j)-c(i,j)-d(i,j);endend%初始时刻地层压力p=Pini*ones(52,1);%系数矩阵 AA=zeros(52);%第 9 行A(1,1)=e(9,6);A(1,2)=b(9,6);A(1,6)=d(9,6);for i=2:4A(i,i-1)=a(9,i+5);A(i,i)=e(9,i+5);A(i,i+1)=b(9,i+5);A(i,i+5)=d(9,i+5);endA(5,4)=a(9,10);A(5,5)=e(9,10)+b(9,10);A(5,10)=d(9,10);%第 8 行A(6,1)=c(8,6);A(6
6、,6)=e(8,6);A(6,7)=b(8,6);A(6,12)=d(8,6);for i=7:9A(i,i-5)=c(8,i);A(i,i-1)=a(8,i);A(i,i)=e(8,i);A(i,i+1)=b(8,i);A(i,i+6)=d(8,i);endA(10,5)=c(8,10);A(10,9)=a(8,10);A(10,10)=e(8,10)+b(8,10);A(10,16)=d(8,10);%第 7 行A(11,11)=e(7,5);A(11,12)=b(7,5);A(11,20)=d(7,5);for i=12:15A(i,i-6)=c(7,i-6);A(i,i-1)=a(7,
7、i-6);A(i,i)=e(7,i-6);A(i,i+1)=b(7,i-6);A(i,i+9)=d(7,i-6);endA(16,10)=c(7,10);A(16,15)=a(7,10);A(16,16)=e(7,10)+b(7,10);A(16,25)=d(7,10);%第 6 行A(17,17)=e(6,2)+a(6,2);A(17,18)=b(6,2);A(17,26)=d(6,2);for i=18:19A(i,i-1)=a(6,i-15);A(i,i)=e(6,i-15);A(i,i+1)=b(6,i-15);A(i,i+9)=d(6,i-15);endfor i=20:23A(i,
8、i-9)=c(6,i-15);A(i,i-1)=a(6,i-15);A(i,i)=e(6,i-15);A(i,i+1)=b(6,i-15);A(i,i+9)=d(6,i-15);end%w2 井定井底流压生产A(24,15)=c(6,9);A(24,23)=a(6,9);A(24,24)=e(6,9)-(3600e-9)*2*pi*K(6,9)*dt/u/C/Fai(6,9)/dx/dy/log(re/rw);A(24,25)=b(6,9);A(24,33)=d(6,9);A(25,16)=c(6,10);A(25,24)=a(6,10);A(25,25)=e(6,10)+b(6,10);A(
9、25,34)=d(6,10);%第 5 行A(26,17)=c(5,2);A(26,26)=e(5,2)+a(5,2);A(26,27)=b(5,2);A(26,35)=d(5,2);for i=27:31A(i,i-9)=c(5,i-24);A(i,i-1)=a(5,i-24);A(i,i)=e(5,i-24);A(i,i+1)=b(5,i-24);A(i,i+9)=d(5,i-24);endfor i=32:33A(i,i-9)=c(5,i-24);A(i,i-1)=a(5,i-24);A(i,i)=e(5,i-24)+d(5,i-24);A(i,i+1)=b(5,i-24);endA(3
10、4,25)=c(5,10);A(34,33)=a(5,10);A(34,34)=e(5,10)+b(5,10)+d(5,10);%第 4 行A(35,26)=c(4,2);A(35,35)=e(4,2)+a(4,2);A(35,36)=b(4,2);A(35,41)=d(4,2);for i=36:39A(i,i-9)=c(4,i-33);A(i,i-1)=a(4,i-33);A(i,i)=e(4,i-33);A(i,i+1)=b(4,i-33);A(i,i+6)=d(4,i-33); endA(40,31)=c(4,7);A(40,39)=a(4,7);A(40,40)=e(4,7)+b(4
11、,7);A(40,46)=d(4,7);%第 3 行A(41,35)=c(3,2);A(41,41)=e(3,2)+a(3,2);A(41,42)=b(3,2);A(41,47)=d(3,2);for i=42:45 A(i,i-6)=c(3,i-39);A(i,i-1)=a(3,i-39);A(i,i)=e(3,i-39);A(i,i+1)=b(3,i-39);A(i,i+6)=d(3,i-39); endA(46,40)=c(3,7);A(46,45)=a(3,7);A(46,46)=e(3,7)+b(3,7);A(46,52)=d(3,7);%第 2 行A(47,41)=c(2,2);A
12、(47,47)=e(2,2)+a(2,2)+d(2,2);A(47,48)=b(2,2);for i=48:51A(i,i-6)=c(2,i-45);A(i,i-1)=a(2,i-45);A(i,i)=e(2,i-45)+d(2,i-45);A(i,i+1)=b(2,i-45);endA(52,46)=c(2,7);A(52,51)=a(2,7);A(52,52)=e(2,7)+b(2,7)+d(2,7);% 循环次数 tntn=0;while(tnn)%右端项 BB=-p;%第 9 行B(1)=B(1)-c(9,6)*Pini-a(9,6)*Pini;for i=2:5B(i)=B(i)-c
13、(9,i+5)*Pini;end%第 8 行B(6)=B(6)-a(8,6)*Pini;%第 7 行B(11)=B(11)-c(7,5)*Pini-a(7,5)*Pini;%第 6 行for i=17:19B(i)=B(i)-c(6,i-15)*Pini;end%w2 井定井底流压生产B(24)=B(24)-(3600e-9)*2*pi*K(6,9)*dt/u/C/Fai(6,9)/dx/dy/log(re/rw)*Pwf2;%W1 井定产生产B(44)=B(44)+dt*Q1/24/C/Fai(3,5)/H(3,5)/dx/dy; %计算未知量压力 p1p1=AB;%稳定条件 压力变化最大值
14、小于 0.000001if max(abs(p1-p)0.000001break;endp=p1;tn=tn+1;end%将迭代时间换算为天d=tn*dt/24;%将计算出的压力写入地层压力 PP(9,6:10)=p(1:5);P(8,6:10)=p(6:10);P(7,5:10)=p(11:16);P(6,2:10)=p(17:25);P(5,2:10)=p(26:34);P(4,2:7)=p(35:40);P(3,2:7)=p(41:46);P(2,2:7)=p(47:52);%计算 W1 井底流压。由产量公式：Q=2KH(P-P_wf )/(ln （re/rw ） )得：W1 井底流压：Pwf1=P1-Q1ln （re/rw）/2 KH Pwf1=P(3,5)-Q1*u*log(re/rw)/(2*pi*K(3,5)*H(3,5)/86400*1e9;%W2 井产油量：Q2=2 KH(P2-Pwf2 )/(ln（re/rw ） )Q2=2*pi*K(6,9)*H(6,9)*(P(6,9)-Pwf2 )/(u*log(re/rw)*1e-9*86400;
