Rescaled exponential and density-based decline models: Extension to variable- rate/pressure-drawdown conditions

Constant-bottomhole-pressure (BHP) solutions to the diffusivity equation are used routinely for the analysis of well-decline performance in boundary-dominated flow (BDF). Gas-well-performance equations for constant-BHP conditions may be written in a number of ways, including rate vs. pseudopressure, rate vs. pseudotime, rate vs. material-balance pseudotime expressions, and, more recently, in terms of density-based rescaled exponential models (Ayala and Ye 2013a, b; Ye and Ayala 2013). A significant constraint for some of these models, especially for the rescaled exponential model, is the assumption that BHP conditions remain constant throughout the declining life of the well. However, the most realistic well-specification scenario is that in which both BHP and flow rate decline in time (i.e., a variablepressure- drawdown/-rate condition). In this study, we explore and prove the validity of rescaled exponential and density-based gas decline models for the analysis of variable-rate/pressure-drop gas systems in BDF. We also demonstrate that the constant-rate and constant-BHP solutions given by the proposed density-based decline models for gas wells under BDF are interchangeable.