Consider that the BOP working pressure of $5,000$ psi was selected. For the selection, the drilling engineer assumed the well full of gas at an anticipated depth of $10,000$ ft$,$ gas gradient equal to $0\mathrm{.}1$ psi$/$ft$,$ and pore pressure equal to $5,000$ psi at $10,000$ ft$.$ This is equivalent to a density of $9\mathrm{.}6$ ppg as pore pressure.

When the well reaches $10,000$ ft$,$ the geologist tells you that he wants to drill deeper. Considering that the pore pressure is constant and equal to $9\mathrm{.}6$ ppg with increasing depth, determine the maximum depth $($TVD$)$ you can go assuming that you will have the well full of gas at TVD$.$

Answer is $12525$ ft$,$ please show steps