Derive the MBE for a tank with rigid and incompressible walls $($i$.$e$.$ tank volume remains constant regardless of the fluid pressure inside$)$ for the cases of different conditions shown below.

a$.$ The tank is initially full of oil with some slightly compressible solids occupying $78\%$ of tank volume at pi$.$ Some oil is bleeded to reduce the pressure to p$1.$ The removed oil from the tank is collected as $N_p$ STB of oil and the related $G_p$ SCF of gas at surface conditions.

b$.$ The tank is initially full of oil and gas at pi and there is no solids in$.$ While some oil is bleeded from the bottom valve, simultaneaouly some gas is removed from top valve reducing the pressure in the tank to $p_1.$ The removed oil from the tank is collected as $N_p$ STB of oil and $G_{p1}$ SCF of gas at surface conditions. The removed gas is collected

as $G_{p_{2}2}SCF$ at surface conditions. We also know that $p_b>p_i>p_1.$ In your derivation use the symbol $R_p$ as cumulative produced gas oil ratio.