Observe numerically the limit of the pressure for large times. Explain its value.
Implement the code in scilab. Debug it and run it. The code of programs attached in mail. Observe numerically the limit of the pressure for large times. Explain its value. The limit of the pressure for large time is pressure of well. Because if the pressure of reservoir less than wells pressure will be no fluid flow in the wellbore (The data on the compressibility of missing so I took = 1.0E-6). Look at figure 1.
Figure1. The modeling time is 8 year. The pressure of reservoir approximately equal the wells pressure. 3. Plot the instantaneous flow rate at the well function of time. Look at figure 2.
Figure 2. Instantaneous flow rate at the well function of time 4. Plot the ratio of the produced oil wrt the initial oil in place function of time. Look at figure3.
Figure 3. The ratio of the produced oil wrt the initial oil in place function of time
5. Observe numerically the limit of After 8 year, we can see numerical solution for:
Analytically solution for
but
Consequently
Analytically solution for
For solving equation (4) we can primitive function from
6. Run the simulation for different choices of the time and space discretizations ( Table 1. The results of calculation
If time step is increasing then increase the production history
|
and 
for large times. Is it possible to compute analytically these limits when time tends to infinity?
= 0.0000018
= 0.6325262
:
:
, but 
and time step). Comment the convergence of the production history 
. If 
