$(30$ points$)$

$4.$ A production well with wellbore radius of $0\mathrm{.}3ft,$ producing oil at a surface rate of $200$ stb$/$d$,$ drilled and completed in a reservoir with $=0\mathrm{.}16,r_e=6100ft,h=85ft$ and $C_1=1\mathrm{.}2E-05{}^{-1}$ is being pressure tested for $200$ hours $($see the table below$).$ As a Reservoir Engineer you have been asked to analyze this test in order to obtain permeability, skin, apparent radius, wellbore storage $(C_D),$ end of wellbore storage effects, and radius of investigation during the test. $({}_o=0\mathrm{.}7cp$ and $B_o=1\mathrm{.}2r\frac{b}{s}tb)$

$\backslash$table$[[$Time $($hrs$),q{r}_r(st\frac{b}{d}),$Pressure $($psia$)],[00\mathrm{.}00,000\mathrm{.}00,1352\mathrm{.}00],[00\mathrm{.}01,000\mathrm{.}10,1351\mathrm{.}97],[00\mathrm{.}02,000\mathrm{.}90,11351\mathrm{.}68],[00\mathrm{.}03,001\mathrm{.}90,1351\mathrm{.}31],[00\mathrm{.}07,010\mathrm{.}00,1348\mathrm{.}18],[00\mathrm{.}90,080\mathrm{.}00,1317\mathrm{.}52],[02\mathrm{.}00,150\mathrm{.}00,1285\mathrm{.}03],[04\mathrm{.}00,200\mathrm{.}00,1260\mathrm{.}02],[06\mathrm{.}00,200\mathrm{.}00,1258\mathrm{.}45],[10\mathrm{.}00,200\mathrm{.}00,1256\mathrm{.}47],[20\mathrm{.}00,200\mathrm{.}00,1253\mathrm{.}79],[30\mathrm{.}00,200\mathrm{.}00,1252\mathrm{.}22],[40\mathrm{.}00,200\mathrm{.}00,1251\mathrm{.}10],[50\mathrm{.}00,200\mathrm{.}00,1250\mathrm{.}24],[60\mathrm{.}00,200\mathrm{.}00,1249\mathrm{.}53],[70\mathrm{.}00,200\mathrm{.}00,1248\mathrm{.}93],[100\mathrm{.}00,200\mathrm{.}00,1247\mathrm{.}55],[150\mathrm{.}00,200\mathrm{.}00,1245\mathrm{.}98],[200\mathrm{.}00,200\mathrm{.}00,1244\mathrm{.}87]]$