Rigorous and Explicit Determination of Reserves and Hyperbolic Exponents in Gas-Well Decline Analysis

Abstract

Summary Reservoir evaluation on the basis of rate-time data of gas wells producing under boundary-dominated flow (BDF) is often performed with the Arps’ empirical hyperbolic decline model and associated type curves. In this study, we show that, for volumetric, single-phase, gas reservoirs produced at constant bottomhole pressure, the decline exponent, b, used in Arps’ hyperbolic model can be calculated solely on the basis of fluid properties and the prevailing bottomhole specification—regardless of reservoir properties and before collecting any rate-time data. For the case of real gases produced under less-than wide-open decline, the assumption of a constant b necessary for the use of Arps’ equations does not hold true throughout the production life of a reservoir. We show that during early BDF, a hyperbolic window may be defined for which the constant-b assumption may be valid. Within this window, we show that the application of type-curve and straight-line analysis techniques derived from the hyperbolic model can be used to successfully and explicitly determine reservoir properties, including original gas in place (OGIP). Several case studies based on numerical simulation and field data are presented to thoroughly validate and highlight the predictive capabilities of the proposed model.