Advanced Gas Material Balance in Simplified Format

Material balance has long been used in reservoir engineering practice as a simple yet powerful tool to determine the original gas in place (G). The conventional format of the gas material balance equation is the simple straight line plot of p/Z vs. cumulative gas production (G(p)), which can be extrapolated to zero p/Z to obtain G. The graphical simplicity of this method makes it popular. The method was developed for a "volumetric" gas reservoir. It assumes a constant pore volume (PV) of gas and accounts for the energy of gas expansion, but it ignores other sources of energy, such as the effects of formation compressibility, residual fluids expansion and aquifer support. It also does not include other sources of gas storage, such as connected reservoirs or adsorption in coal/shale. In the past, researchers have introduced modified gas material balance equations to account for these other sources of energy. However, the simplicity of the p/Z straight line is lost in the resulting complexity of these equations. In this paper, a new format of the gas material balance equation is presented, which recaptures the simplicity of the straight line while accounting for all the drive mechanisms. This new method uses a p/Z** instead of p/Z. The effect of each of the previously mentioned drive mechanisms appears as an effective compressibility term in the new gas material balance equation. Also, the physical meaning of the effective compressibilities are explained and compared with the concept of drive indices. Furthermore, the gas material balance is used to derive a generalized rigorous total compressibility in the presence of all the previously mentioned drive mechanisms, which is important in calculating the pseudotime used in rate transient analysis of production data.