Arps’ hyperbolic model has historically been used to analyze and forecast gas well performance. This is largely due to its simplicity and explicit nature. Unfortunately, because of the variations of viscosity-compressibility product with average reservoir pressure during boundary-dominated flow (BDF) period, the Arps’ hyperbolic model overestimates gas reserves and future rates. Consequently, existing rate-decline models rely heavily on pseudotime. Unfortunately, pseudotime requires iteration, which is time-consuming.
This paper proposes an empirical rate-decline model for a gas well producing at a constant pressure during BDF. The proposed model utilizes a drawdown correlating parameter that accounts for formation and water compressibilities, as well as the variations of gas properties with pressure. Due to its explicit nature, the proposed rate-decline model can be used to forecast future gas well performance. An explicit model for estimating the decline exponent for a gas well is also proposed. In addition, this paper presents a semi-empirical flowing material balance (SE-FMB) method that allows the estimation of initial gas-in-place, real gas productivity index and estimated ultimate recovery. The advantages of the proposed SE-FMB over the existing methods are two-folds: first, it is iterationless; and second, it avoids the use of a functional relation (or curve fitting) of viscosity-compressibility product and pressure.
The results of this study suggest that the decline exponent for a gas well is time-independent at early-time BDF period and time-dependent at late-time BDF period. At very late-time BDF period, the decline exponent tends to zero. Thus, gas well production data exhibit a hyperbolic decline at early-time BDF period and a transition period at late-time BDF period. At very late-time BDF period, an exponential decline is expected. While the exponential-decline period is not observed in practice due to economic-rate constraints, the hyperbolic-decline period is observed in practice. The transition period may or may not be observed in practice depending on the magnitude of the drawdown parameter and the economic-rate constraints. Comparison of the models results indicates that the proposed rate-decline and the classical Arps’ hyperbolic models are consistent with the rate history during the hyperbolic-decline period; however, the proposed rate-decline model out-performs the classical Arps’ hyperbolic model when the transition period prevails. The results of this study also indicate that ignoring the formation and water compressibilities lead to an overestimation of gas reserves even for a normally-pressured gas reservoir. Simulated and field data have been used to demonstrate the validity and applicability of the proposed model and analysis method.