a$.$ An oil well in the middle of a large reservoir which is actively supported by water drive, has been openhole tested and yields the following data:

$Bo=1\mathrm{.}2$

$=0\mathrm{.}8cp$

$rw=3$ inches

Thickness of interval tested $h=50ft$

$Pwf=3800$ psig $atq=3000ST\frac{B}{d}$

It is estimated that the reservoir has a drainage radius of at least $1000ft.$ Pressure survey both prior to and on build$-$up after the test indicate an original$/$static reservoir pressure of $4500$ psig. The well can be assumed to penetrate the reservoir vertically. Because of the water drive you can assume that the reservoir performance can be modelled by a steady state flow model which gives the following equation:

$P_e-P_w=141\mathrm{.}2\frac{q{B}_v}{Kh}*ln\frac{r_e}{r_w}$

Calculate the reservoir permeability and PI assuming no damage to the reservoir.

b$.$ For the well described in $($a$),$ calculate the relationship between Pwf and q$.$ What would be the pressure Pwf for flowrates of $1000,2000,4000$ and $5000$ STB$/$d$?$

c$.$ Assuming that a larger tubing diameter than that used for the well test can be used, allowing a bottom hole pressure of $2500$ psig to be obtained, what would be the flowrate?