A cylindrical well has a radius of $1,000,$ a well radius of $0\mathrm{.}3$ and thickness of $300.$ The rock

permeability is $50$ mD and the initial pressure is $5,000$ psi. The wellbore is vertical with a length of

$10,000,$ an SSSV set at $1,000$ and an ESP set at $9,500.$ The separator is set next to the wellhead

and it is adjusted at $300$ psi. The SSSV causes a pressure drop of $100$ psi. The ESP is set to carry a

flowrate of $5,000$ stb$/$d by increasing its pressure by $1,000$ psi. The reservoir fluid has a Bo value

of $1\mathrm{.}2$ rb$/$stb and a viscosity value of $2$ cp$.$ Its density along the wellbore is assumed to be constant

and equal to $7$ ppg$.$ The frictional pressure loss is $10-5$ psi$/$ft$/($stb$/$d$).$

$1.$ Draw the pressure profile in the reservoir

$2.$ Draw the pressure profile in the tubing

$3.$ Compute the required pressure loss at the choke so as the meet the separator pressure

requirement

$4.$ How much is going to be the production rate is the choke is fully opened