Nonstatic Pressure History Analyses for Gas Reservoirs

A method has been developed for using nonstatic pressure measurements directly in gas reservoir material balances composed of various energy mechanisms. Applying this method leads to simultaneous determinations of the reservoir p history, gas in place, and other parameters relevant to water influx and effective compressibility. Well-known methods of determining average static pressure, p, have at least two shortcomings:an estimation of reservoir shape andan often-neglected implicit relationship between p and the viscosity-compressibility product. Errors resulting from these deficiencies are minimized by the proposed method through a simple coupling of the well-known pseudo steady-state flow and material-balance equations. The solution of this coupling is obtained through nonlinear regression, and it allows simultaneous evaluations of gas initially in place, static pressure history, and several other reservoir parameters. These parameters can include the initial reservoir pressure, a stabilized gas-deliverability constant, the effective compressibility, aquifer diffusivity, and aquifer volume plus water-influx constants. The results of applying the method to six published cases are presented to illustrate the utility of the method. Introduction Before performing material-balance calculations, separate determinations of the average static reservoir pressure history from available drawdown and buildup tests and shut-in or flowing gradient surveys were required. Well-known methods used for these determinations have been shown by Matthews et al., Odeh and Al-Hussainy, Brons and Miller, and Dietz. All these methods for determining p have one or more undesirable requirements such as a preknowledge of the hydraulic diffusivity in terms of the reservoir area and the reservoir boundary shape plus the assumption of a volumetric depletion-type reservoir-drive mechanism. An additional drawback is found in the implicit relationship between p and the viscosity-compressibility product of the dimensionless time parameter. This product must be evaluated at p in the aforememtioned methods; therefore, the solution of p is implicit. Kazemi has discussed this problem for both oil and gas cases. The proposed method eliminates the intermediate steps in determining a p history before calculating material balances, and it does not require a preknowledge of the hydraulic diffusivity, boundary shape, or reservoir-drive mechanism. Part of the original development work on this problem was presented by Garb et al. This publication showed an iterative method that coupled the functional p terms of the material-balance and the pseudosteady-state flow equations for drawdown and buildup cases. However, the method was limited to determining only gas initially in place for normalpressured, nonwater-drive reservoirs. The new development formulates the problem in a different manner to obtain nonlinear solutions in various reservoir-drive mechanisms. This method eliminates the prerequisite of p determinations, and it provides simultaneous solutions of gas initially in place, p history, water influx, and effective rock and connate water compressibilities. SPEJ P. 209^