Performance Analysis of Gas Wells Based on the Conventional Decline Parameters and the Flow Integral Equation

Abstract

The estimation of reserves and performance prediction are two vital tasks for the development of gas reservoirs where the evaluation of gas in place or well-controlled reserves, as the foundation of the performance analysis of gas wells, turns to be exceedingly significant. Advanced production data analysis or modern rate transient analysis (RTA) methods mainly depend on the iterative calculations of material balance quasitime (tca) and type curve fitting, the essence of which is to update the average reservoir pressure data time and again. The traditional Arps’ decline models are of empirical nature despite the convenience and applicability to the constant bottomhole pressure (BHP) condition. In order to avoid the implicit iteration, this paper develops an explicit method for estimating the average reservoir pressure on the basis of dynamic material balance equation (DMBE), termed “flow integral method,” which can be applied to various gas production systems under boundary-dominated flow (BDF). Based on the flow integral method and the decline parameter evaluation, we employ the hyperbolic decline model to model the gas well performance at a constant BHP. The analytical formulations of decline rate and decline exponent are deduced from the DMBE and the static material balance equation (SMBE) considering the elastic compressibilities of rock pore and bound water. The resulting decline parameter method for explicit estimation of gas reserves boasts a solid and rigorous theory foundation that production rate, decline rate, and average reservoir pressure profiles have reference to each other, and its implementation steps are explained in the paper. The SMBE can, combined with the estimated pressure profile by the flow integral method, also be used to determine gas reserves which is not limited to the constant-BHP condition and can calibrate the estimates of the decline parameter method. The proposed methods are proven effective and reliable with several numerical cases at different BHPs and a field example.