Rescaled Exponential and Density-Based Decline Models: Extension toVariable Rate/Pressure-Drawdown Conditions

Abstract

Summary Constant-bottomhole-pressure (BHP) solutions to the diffusivity equation areused routinely for the analysis of well-decline performance inboundary-dominated flow (BDF). Gas-well-performance equations for constant-BHPconditions may be written in a number of ways, including rate vs.pseudopressure, rate vs. pseudotime, rate vs. material-balance pseudotimeexpressions, and, more recently, in terms of density-based rescaled exponentialmodels (Ayala and Ye 2013a, b; Ye and Ayala 2013). A significant constraint forsome of these models, especially for the rescaled exponential model, is theassumption that BHP conditions remain constant throughout the declining life ofthe well. However, the most realistic well-specification scenario is that inwhich both BHP and flow rate decline in time (i.e., avariable-pressure-drawdown/-rate condition. In this study, we explore and provethe validity of rescaled exponential and density-based gas decline models forthe analysis of variable-rate/pressure-drop gas systems in BDF. We alsodemonstrate that the constant-rate and constant-BHP solutions given by theproposed density-based decline models for gas wells under BDF areinterchangeable.