$$ We are drilling at $10000$ ft in a formation with $20\%$ porosity, $30\%$ water saturation and $70\%$ gas saturation. The temperature is $640$ R$,$ and the mud density is $11$ ppg$.$ The gas gravity is $\mathrm{.}72.$ The drilling rate is $100$ ft$/$hr with a $1214$ inch bit. The circulation rate is $300$ gpm$.$ Formation water is $9\mathrm{.}04$ ppg$,$ and formation rock density is $26$ ppg$.$

a$.$ What is the mud density at the surface? Ppg

b$.$ What is the average density of the annular mud?

c$.$ At what rate $($SCFD$)$ will gas be liberated at the surface?