$($ Petroleum engineering Qs $-$ Integrated Reservoir management$)$The material balance equation is one of the reliable approaches used by reservoir engineers to estimate initial gas in place when enough production$-$pressure history is available. Consider below volumetric gas reservoir with production history data as shown in the below Table:

$\backslash$table$[[$Time$,$ years,Reservoir Pressure, psia,Cumulative production, MMscf$],[0,2100,0],[1,2008,1\mathrm{.}4],[2,1983,2\mathrm{.}5],[3,1721,3\mathrm{.}7],[4,1564,4\mathrm{.}2]]$

The porosity, initial water saturation, cross$-$sectional area, pay thickness, temperature, and specific gravity of gas are $20\%,0\mathrm{.}4,1080$ acres, $40ft,160F,$ and $0\mathrm{.}72$ respectively. Identify the differences of gas initially in place between volumetric and $\frac{p}{z}$ method.