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3. Consider the single phase, incompressible flow of oil taking place in the 2D, homogeneous, isotropic system shown in the following figure. Assume

1000=Δ=Δ yx ft, 50=h ft, and 100== yx kk md. A production well in the center

gridblock is produced at a rate of 12000 STB/D ( 2=oμ cp). If the pressure in the

boundary gridblocks is kept at 2000 psia, calculate the pressure distribution in the system and the flowing surface pressure in the wellbore.

Discretized 2D reservoir in Problem 3.

4. Consider the 1D, single phase, steady-state flow of oil in the horizontal, heterogeneous system shown in figure below. The following table gives the gridblock properties. The boundary conditions are as follows.

(a) Pressure in Gridblock 1 is maintained at 3000 psia. (b) Production rate from Gridblock 2 is specified as 1000 STB/D. (c) The pressure gradient at the extreme right of the system is given as 0.2 psi/ft.

The fluid properties are 2=oμ cp and 0.1=oB RB/STB. With the appropriate PDE and

its finite difference approximation, calculate the pressure distribution in the system.

Discretized 1D reservoir in Problem 4.

Gridblock properties for Problem 4.

Gridblock xΔ (ft) h (ft) w (ft) xk md)

1 200 40 100 200 2 400 60 100 160 3 300 20 100 180