油藏数值模拟隐式差分MATLAB源程序

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 0;3

2、30 330 290 270 250 230 205 197.5 180 185 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Fai=

3、(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=2:9 for j=2:10 a(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

4、)+H(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,

5、j)*K(i,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)

6、;A(6,6)=e(8,6);A(6,7)=b(8,6);A(6,12)=d(8,6);for i=7:9 A(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=12:15 A(i,i-6)=c(7,i-6); A(i,

7、i-1)=a(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=18:19 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

8、for i=20:23 A(i,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)

9、=e(6,10)+b(6,10);A(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=27:31 A(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=32:33 A(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);

10、 A(i,i+1)=b(5,i-24);endA(34,25)=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=36:39 A(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(40,3

11、9)=a(4,7);A(40,40)=e(4,7)+b(4,7);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)

12、=d(3,7);%第2行A(47,41)=c(2,2);A(47,47)=e(2,2)+a(2,2)+d(2,2);A(47,48)=b(2,2);for i=48:51 A(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

13、(9,6)*Pini;for i=2:5 B(i)=B(i)-c(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=17:19 B(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 压力变化最大值小于0.000001if max(abs(p1-p)0.000001 break;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：