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 and for large times. Is it possible to compute analytically these limits when time tends to infinity?

After 8 year, we can see numerical solution for:

= 0.0000018

= 0.6325262

Analytically solution for :

but

Consequently

 

Analytically solution for :

 

For solving equation (4) we can primitive function from , but have not explicit decision (5). And we cannot find analytically the limit of

 

 

6. Run the simulation for different choices of the time and space discretizations ( and time step). Comment the convergence of the production history

Table 1. The results of calculation

	Time step
	0.2*3600*24	0.2389241
	0.2*3600*24	0.2896715
	2*3600*24	0.3013651
	2*3600*24	0.3111415
	20*3600*24	0.3099529
	20*3600*24	0.3132934
	20*3600*24	0.3152983

If time step is increasing then increase the production history . If
is increasing then increase .