I have translated the tex from the previous post to the "brand" that is used on this forum.
The 3 equations are:
Mass conservation laws for water and for CO2:
The Darcy Law for both phases, water and gas is
Initial and boundary conditions
(x is distance and t is time,P is pressure,s is saturation):
At t=0, s=1
At x=0. s=s_wi
At x=0, P=P_1
At x=L, P=P_2
Three variables to be found:
F is a function of s and F is ratio of relative premeability and viscosity.
All others are known....rw and rg are relative premeabilities for water and gas...
and are viscosities for water and gas.
Numerical solution adopted by me:
Consider finite steps,
and the same for P and u.
Then (for the explicit method), we can write approximately using discretization as
On substitution in (1), we get an equation for s at (i,k+1) .
Now , i tried to do the same for the other 2 equations but could not separate the
variables u and p.Also did not know how to use the initial and boundary conditions.
But i think the procedure could be like:
The solution at the layer k=0 (t=0) is known from initial conditions.
Assume that the solution at layer k has been calculated. In order to find the solution at the layer k+1,
1) Find the values of saturation , for each i, from Eq. (s);
2) Find the values of from Eq. (r);
3) Re-calculate based on the known values of ;
4) Find the values of from Eq. (u).
So , please help me as its urgent...thank you so much...