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Kz_446.m
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Kz_446.m
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%z diretion 4*4*6 upscaling
ny_446=55;
nx_446=15;
nz_446=15;
kz_new=zeros(ny_446,nx_446,nz_446);
% left trans for constant pressure on left side x=0
%layers 1-3
for k=1:6:25
for i=1:4:ny
for j=1:4:nx
nx_d=4;
ny_d=4;
nz_d=6;
Tx_d=zeros(ny_d,nx_d+1,nz_d);
for k1=1:nz_d
for i1=1:ny_d
j1=1;
Tx_d(i1,j1,k1)=0;
end
end
% trans for x=right side
for k1=1:nz_d
for i1=1:ny_d
j1=nx_d+1;
Tx_d(i1,j1,k1)=0;
end
end
% trans for x direction for cells i between
k2=k;
for k1=1:nz_d
i2=i;
for i1=1:ny_d
j2=j+1;
for j1=2:nx_d
T1=(2*0.00633*400*kx(i2,j2-1,k2)/20^2);
T2=(2*0.00633*400*kx(i2,j2,k2)/20^2);
Tx_d(i1,j1,k1)=T1*T2/(T1+T2);
if Tx_d(i1,j1,k1)==0
Tx_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
k2=k2+1;
end
Ty_d=zeros(ny_d+1,nx_d,nz_d);
% south T=0
for k1=1:nz_d
for j1=1:nx_d
i1=1;
Ty_d(i1,j1,k1)=0;
end
end
%north T=0
for k1=1:nz_d
for j1=1:nx_d
i1=ny_d+1;
Ty_d(i1,j1,k1)=0;
end
end
% T in y direction for rest of the cells
k2=k;
for k1=1:nz_d
i2=i+1;
for i1=2:ny_d
j2=j;
for j1=1:nx_d
T1=(2*0.00633*400*ky(i2-1,j2,k2)/10^2);
T2=(2*0.00633*400*ky(i2,j2,k2)/10^2);
Ty_d(i1,j1,k1)=T1*T2/(T1+T2);
if Ty_d(i1,j1,k1)==0
Ty_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
k2=k2+1;
end
% Top T is face trans
Tz_d=zeros(ny_d,nx_d,nz_d+1);
i2=i;
k2=k;
for i1=1:ny_d
j2=j;
for j1=1:nx_d
k1=1;
Tz_d(i1,j1,k1)=(2*0.00633*400*kz(i2,j2,k2)/2^2);
if Tz_d(i1,j1,k1)==0
Tz_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
% bottom T is face trans
i2=i;
k2=k+nz_d-1;
for i1=1:ny_d
j2=j;
for j1=1:nx_d
k1=nz_d+1;
Tz_d(i1,j1,k1)=(2*0.00633*400*kz(i2,j2,k2)/2^2);
if Tz_d(i1,j1,k1)==0
Tz_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
% Tz for between cells
k2=k+1;
for k1=2:nz_d
i2=i;
for i1=1:ny_d
j2=j;
for j1=1:nx_d
T1=(2*0.00633*400*kz(i2,j2,k2-1)/2^2);
T2=(2*0.00633*400*kz(i2,j2,k2)/2^2);
Tz_d(i1,j1,k1)=T1*T2/(T1+T2);
if Tz_d(i1,j1,k1)==0
Tz_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
k2=k2+1;
end
N=(nx_d)*(ny_d)*(nz_d);
%i+1 diagonal
a=0;
l=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
l(a,1)=-Tx_d(i1,j1+1,k1);
end
end
end
%i-1 diagonal
a=0;
n=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
n(a,1)=-Tx_d(i1,j1,k1);
end
end
end
%j+1 diagonal
a=0;
p=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
p(a,1)=-Ty_d(i1+1,j1,k1);
end
end
end
% j-1 diagonal
a=0;
q=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
q(a,1)=-Ty_d(i1,j1,k1);
end
end
end
%k+1 diagonal
a=0;
r=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
if k1==nz_d
r(a,1)=0;
else
r(a,1)=-Tz_d(i1,j1,k1+1);
end
end
end
end
% k-1 diagonal
a=0;
s=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
if k1==1;
s(a,1)=0;
else
s(a,1)=-Tz_d(i1,j1,k1);
end
end
end
end
%Center diagonal
a=0;
c=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
c(a,1)=Tz_d(i1,j1,k1)+Tz_d(i1,j1,k1+1)+Ty_d(i1,j1,k1)+Ty_d(i1+1,j1,k1)+Tx_d(i1,j1,k1)+Tx_d(i1,j1+1,k1);
end
end
end
% Transmissibility matrix
B=[ r p l c n q s];
T=spdiags(B,[-nx_d*ny_d,-nx_d,-1,0,1,nx_d,nx_d*ny_d],nx_d*ny_d*nz_d,nx_d*ny_d*nz_d);
a=0;
D_d=zeros(nx_d*ny_d*nz_d,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
if k1==1
D_d(a,1)=Tz_d(i1,j1,k1);
else
D_d(a,1)=0;
end
end
end
end
P=T\sparse(D_d);
P=full(P);
P=reshape(P,nx_d,ny_d,nz_d);
for k1=1:nz_d
P1(:,:,k1)=P(:,:,k1)';
end
%rate calculation
k1=1;
q_d=0;
for i1=1:ny_d
for j1=1:nx_d
q_d=q_d+Tz_d(i1,j1,k1)*(1-P1(i1,j1,k1));
end
end
kz_new(floor(i/4)+1,floor(j/4)+1,floor(k/6)+1)= q_d*nz_d*2/(nx_d*20*ny_d*10*0.00633);
end
end
end
% layers 31-35
k=31;
for i=1:4:ny
for j=1:4:nx
nx_d=4;
ny_d=4;
nz_d=5;
Tx_d=zeros(ny_d,nx_d+1,nz_d);
for k1=1:nz_d
for i1=1:ny_d
j1=1;
Tx_d(i1,j1,k1)=0;
end
end
% trans for x=right side
for k1=1:nz_d
for i1=1:ny_d
j1=nx_d+1;
Tx_d(i1,j1,k1)=0;
end
end
% trans for x direction for cells i between
k2=k;
for k1=1:nz_d
i2=i;
for i1=1:ny_d
j2=j+1;
for j1=2:nx_d
T1=(2*0.00633*400*kx(i2,j2-1,k2)/20^2);
T2=(2*0.00633*400*kx(i2,j2,k2)/20^2);
Tx_d(i1,j1,k1)=T1*T2/(T1+T2);
if Tx_d(i1,j1,k1)==0
Tx_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
k2=k2+1;
end
Ty_d=zeros(ny_d+1,nx_d,nz_d);
% south T=0
for k1=1:nz_d
for j1=1:nx_d
i1=1;
Ty_d(i1,j1,k1)=0;
end
end
%north T=0
for k1=1:nz_d
for j1=1:nx_d
i1=ny_d+1;
Ty_d(i1,j1,k1)=0;
end
end
% T in y direction for rest of the cells
k2=k;
for k1=1:nz_d
i2=i+1;
for i1=2:ny_d
j2=j;
for j1=1:nx_d
T1=(2*0.00633*400*ky(i2-1,j2,k2)/10^2);
T2=(2*0.00633*400*ky(i2,j2,k2)/10^2);
Ty_d(i1,j1,k1)=T1*T2/(T1+T2);
if Ty_d(i1,j1,k1)==0
Ty_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
k2=k2+1;
end
% Top T is face trans
Tz_d=zeros(ny_d,nx_d,nz_d+1);
i2=i;
k2=k;
for i1=1:ny_d
j2=j;
for j1=1:nx_d
k1=1;
Tz_d(i1,j1,k1)=(2*0.00633*400*kz(i2,j2,k2)/2^2);
if Tz_d(i1,j1,k1)==0
Tz_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
% bottom T is face trans
i2=i;
k2=k+nz_d-1;
for i1=1:ny_d
j2=j;
for j1=1:nx_d
k1=nz_d+1;
Tz_d(i1,j1,k1)=(2*0.00633*400*kz(i2,j2,k2)/2^2);
if Tz_d(i1,j1,k1)==0
Tz_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
% Tz for between cells
k2=k+1;
for k1=2:nz_d
i2=i;
for i1=1:ny_d
j2=j;
for j1=1:nx_d
T1=(2*0.00633*400*kz(i2,j2,k2-1)/2^2);
T2=(2*0.00633*400*kz(i2,j2,k2)/2^2);
Tz_d(i1,j1,k1)=T1*T2/(T1+T2);
if Tz_d(i1,j1,k1)==0
Tz_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
k2=k2+1;
end
N=(nx_d)*(ny_d)*(nz_d);
%i+1 diagonal
a=0;
l=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
l(a,1)=-Tx_d(i1,j1+1,k1);
end
end
end
%i-1 diagonal
a=0;
n=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
n(a,1)=-Tx_d(i1,j1,k1);
end
end
end
%j+1 diagonal
a=0;
p=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
p(a,1)=-Ty_d(i1+1,j1,k1);
end
end
end
% j-1 diagonal
a=0;
q=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
q(a,1)=-Ty_d(i1,j1,k1);
end
end
end
%k+1 diagonal
a=0;
r=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
if k1==nz_d
r(a,1)=0;
else
r(a,1)=-Tz_d(i1,j1,k1+1);
end
end
end
end
% k-1 diagonal
a=0;
s=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
if k1==1;
s(a,1)=0;
else
s(a,1)=-Tz_d(i1,j1,k1);
end
end
end
end
%Center diagonal
a=0;
c=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
c(a,1)=Tz_d(i1,j1,k1)+Tz_d(i1,j1,k1+1)+Ty_d(i1,j1,k1)+Ty_d(i1+1,j1,k1)+Tx_d(i1,j1,k1)+Tx_d(i1,j1+1,k1);
end
end
end
% Transmissibility matrix
B=[ r p l c n q s];
T=spdiags(B,[-nx_d*ny_d,-nx_d,-1,0,1,nx_d,nx_d*ny_d],nx_d*ny_d*nz_d,nx_d*ny_d*nz_d);
a=0;
D_d=zeros(nx_d*ny_d*nz_d,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
if k1==1
D_d(a,1)=Tz_d(i1,j1,k1);
else
D_d(a,1)=0;
end
end
end
end
P=T\sparse(D_d);
P=full(P);
P=reshape(P,nx_d,ny_d,nz_d);
for k1=1:nz_d
P1(:,:,k1)=P(:,:,k1)';
end
%rate calculation
k1=1;
q_d=0;
for i1=1:ny_d
for j1=1:nx_d
q_d=q_d+Tz_d(i1,j1,k1)*(1-P1(i1,j1,k1));
end
end
kz_new(floor(i/4)+1,floor(j/4)+1,floor(k/6)+1)= q_d*nz_d*2/(nx_d*20*ny_d*10*0.00633);
end
end
% layers 36-83
for k=36:6:78
for i=1:4:ny
for j=1:4:nx
nx_d=4;
ny_d=4;
nz_d=6;
Tx_d=zeros(ny_d,nx_d+1,nz_d);
for k1=1:nz_d
for i1=1:ny_d
j1=1;
Tx_d(i1,j1,k1)=0;
end
end
% trans for x=right side
for k1=1:nz_d
for i1=1:ny_d
j1=nx_d+1;
Tx_d(i1,j1,k1)=0;
end
end
% trans for x direction for cells i between
k2=k;
for k1=1:nz_d
i2=i;
for i1=1:ny_d
j2=j+1;
for j1=2:nx_d
T1=(2*0.00633*400*kx(i2,j2-1,k2)/20^2);
T2=(2*0.00633*400*kx(i2,j2,k2)/20^2);
Tx_d(i1,j1,k1)=T1*T2/(T1+T2);
if Tx_d(i1,j1,k1)==0
Tx_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
k2=k2+1;
end
Ty_d=zeros(ny_d+1,nx_d,nz_d);
% south T=0
for k1=1:nz_d
for j1=1:nx_d
i1=1;
Ty_d(i1,j1,k1)=0;
end
end
%north T=0
for k1=1:nz_d
for j1=1:nx_d
i1=ny_d+1;
Ty_d(i1,j1,k1)=0;
end
end
% T in y direction for rest of the cells
k2=k;
for k1=1:nz_d
i2=i+1;
for i1=2:ny_d
j2=j;
for j1=1:nx_d
T1=(2*0.00633*400*ky(i2-1,j2,k2)/10^2);
T2=(2*0.00633*400*ky(i2,j2,k2)/10^2);
Ty_d(i1,j1,k1)=T1*T2/(T1+T2);
if Ty_d(i1,j1,k1)==0
Ty_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
k2=k2+1;
end
% Top T is face trans
Tz_d=zeros(ny_d,nx_d,nz_d+1);
i2=i;
k2=k;
for i1=1:ny_d
j2=j;
for j1=1:nx_d
k1=1;
Tz_d(i1,j1,k1)=(2*0.00633*400*kz(i2,j2,k2)/2^2);
if Tz_d(i1,j1,k1)==0
Tz_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
% bottom T is face trans
i2=i;
k2=k+nz_d-1;
for i1=1:ny_d
j2=j;
for j1=1:nx_d
k1=nz_d+1;
Tz_d(i1,j1,k1)=(2*0.00633*400*kz(i2,j2,k2)/2^2);
if Tz_d(i1,j1,k1)==0
Tz_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
% Tz for between cells
k2=k+1;
for k1=2:nz_d
i2=i;
for i1=1:ny_d
j2=j;
for j1=1:nx_d
T1=(2*0.00633*400*kz(i2,j2,k2-1)/2^2);
T2=(2*0.00633*400*kz(i2,j2,k2)/2^2);
Tz_d(i1,j1,k1)=T1*T2/(T1+T2);
if Tz_d(i1,j1,k1)==0
Tz_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
k2=k2+1;
end
N=(nx_d)*(ny_d)*(nz_d);
%i+1 diagonal
a=0;
l=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
l(a,1)=-Tx_d(i1,j1+1,k1);
end
end
end
%i-1 diagonal
a=0;
n=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
n(a,1)=-Tx_d(i1,j1,k1);
end
end
end
%j+1 diagonal
a=0;
p=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
p(a,1)=-Ty_d(i1+1,j1,k1);
end
end
end
% j-1 diagonal
a=0;
q=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
q(a,1)=-Ty_d(i1,j1,k1);
end
end
end
%k+1 diagonal
a=0;
r=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
if k1==nz_d
r(a,1)=0;
else
r(a,1)=-Tz_d(i1,j1,k1+1);
end
end
end
end
% k-1 diagonal
a=0;
s=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
if k1==1;
s(a,1)=0;
else
s(a,1)=-Tz_d(i1,j1,k1);
end
end
end
end
%Center diagonal
a=0;
c=zeros(N,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
c(a,1)=Tz_d(i1,j1,k1)+Tz_d(i1,j1,k1+1)+Ty_d(i1,j1,k1)+Ty_d(i1+1,j1,k1)+Tx_d(i1,j1,k1)+Tx_d(i1,j1+1,k1);
end
end
end
% Transmissibility matrix
B=[ r p l c n q s];
T=spdiags(B,[-nx_d*ny_d,-nx_d,-1,0,1,nx_d,nx_d*ny_d],nx_d*ny_d*nz_d,nx_d*ny_d*nz_d);
a=0;
D_d=zeros(nx_d*ny_d*nz_d,1);
for k1=1:nz_d
for i1=1:ny_d
for j1=1:nx_d
a=a+1;
if k1==1
D_d(a,1)=Tz_d(i1,j1,k1);
else
D_d(a,1)=0;
end
end
end
end
P=T\sparse(D_d);
P=full(P);
P=reshape(P,nx_d,ny_d,nz_d);
for k1=1:nz_d
P1(:,:,k1)=P(:,:,k1)';
end
%rate calculation
k1=1;
q_d=0;
for i1=1:ny_d
for j1=1:nx_d
q_d=q_d+Tz_d(i1,j1,k1)*(1-P1(i1,j1,k1));
end
end
kz_new(floor(i/4)+1,floor(j/4)+1,floor(k/6)+1)= q_d*nz_d*2/(nx_d*20*ny_d*10*0.00633);
end
end
end
% layers 84-85
k=84;
for i=1:4:ny
for j=1:4:nx
nx_d=4;
ny_d=4;
nz_d=2;
Tx_d=zeros(ny_d,nx_d+1,nz_d);
for k1=1:nz_d
for i1=1:ny_d
j1=1;
Tx_d(i1,j1,k1)=0;
end
end
% trans for x=right side
for k1=1:nz_d
for i1=1:ny_d
j1=nx_d+1;
Tx_d(i1,j1,k1)=0;
end
end
% trans for x direction for cells i between
k2=k;
for k1=1:nz_d
i2=i;
for i1=1:ny_d
j2=j+1;
for j1=2:nx_d
T1=(2*0.00633*400*kx(i2,j2-1,k2)/20^2);
T2=(2*0.00633*400*kx(i2,j2,k2)/20^2);
Tx_d(i1,j1,k1)=T1*T2/(T1+T2);
if Tx_d(i1,j1,k1)==0
Tx_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
k2=k2+1;
end
Ty_d=zeros(ny_d+1,nx_d,nz_d);
% south T=0
for k1=1:nz_d
for j1=1:nx_d
i1=1;
Ty_d(i1,j1,k1)=0;
end
end
%north T=0
for k1=1:nz_d
for j1=1:nx_d
i1=ny_d+1;
Ty_d(i1,j1,k1)=0;
end
end
% T in y direction for rest of the cells
k2=k;
for k1=1:nz_d
i2=i+1;
for i1=2:ny_d
j2=j;
for j1=1:nx_d
T1=(2*0.00633*400*ky(i2-1,j2,k2)/10^2);
T2=(2*0.00633*400*ky(i2,j2,k2)/10^2);
Ty_d(i1,j1,k1)=T1*T2/(T1+T2);
if Ty_d(i1,j1,k1)==0
Ty_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
k2=k2+1;
end
% Top T is face trans
Tz_d=zeros(ny_d,nx_d,nz_d+1);
i2=i;
k2=k;
for i1=1:ny_d
j2=j;
for j1=1:nx_d
k1=1;
Tz_d(i1,j1,k1)=(2*0.00633*400*kz(i2,j2,k2)/2^2);
if Tz_d(i1,j1,k1)==0
Tz_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
% bottom T is face trans
i2=i;
k2=k+nz_d-1;
for i1=1:ny_d
j2=j;
for j1=1:nx_d
k1=nz_d+1;
Tz_d(i1,j1,k1)=(2*0.00633*400*kz(i2,j2,k2)/2^2);
if Tz_d(i1,j1,k1)==0
Tz_d(i1,j1,k1)=10^-15;
end
j2=j2+1;
end
i2=i2+1;
end
% Tz for between cells
k2=k+1;
for k1=2:nz_d
i2=i;
for i1=1:ny_d
j2=j;