A cylindrical well has a radius of $3000,$ a well radius of $0\mathrm{.}35$ and thickness of $300.$ The rock permeability is $40$ mD and the initial pressure is $4,520$ psi. The wellbore is vertical with a length of $10,000,$ an SSSV set at $1,000$ causing a pressure drop of $100$psi under flowing conditions. The reservoir fluid has a Bo value of $1\mathrm{.}32$ rb$/$stb and a viscosity value of $21\mathrm{.}5$cp$.$ and a saturation pressure of $593$psi. The liquid phase density along the wellbore is assumed to be constant and equal to $6\mathrm{.}5$ppg$.$ The frictional pressure loss is $0\mathrm{.}8*10-5$ psi$/$ft$/($stb$/$d$).$

$1.$ Compute the expected wellhead pressure when the well is shut in

$2.$ Provide a chart of the pressure from the perforations level up to the wellhead choke when the well is shut in$.$

$3.$ Compute the rexpected wellhead pressure when the well is producing at a rate of$1,000$ stb$/$d

$4.$Can the well produce at a rate of $3,000$ stb$/$dy$?$