Inflow Performance Skin

A well is drilled in a clean sandstone formation. The DLL and FDC$/$CNL logs indicted a productive horizon from $5080-5092\text{'},$ TVD$.$ A sidewall core sample indicates an average permeability of $100md.$ in this horizon and the PVT analysis confirms $B_{\text{@}}$ of $1\mathrm{.}1rs\frac{v}{S}TB.$ Oil viscosity is $1\mathrm{.}3cp.$

$($a$)$ Assuming the drainage radius is $2980ft$ and the wellbore radius is $0\mathrm{.}328ft,$ what is the steady state productivity index $($PI or J$)$ for this well?

$($b$)$ Draw the inflow performance curve for this well if the initial reservoir pressure is $3100$ psi.

$($c$)$ If a subsequent well test confirms an in$-$situ skin of $+8,$ what is the PI for the well taking this skin into account?

$($d$)$ Draw the inflow performance curve for this well taking the positive skin into account.