Approximate analytical solutions of well testing for the reservoir with simple2-dimensional boundary shapes by the radial composite model

Abstract

One-dimensional radial flow equations are equivalent to those of linear flow, which has hyperbolic function of permeability and porosity. In other words, if we consider the permeability and porosity variation for linear direction, we can represent the radial flow. To expand this idea to various types of inner and outer boundary shapes, we defined the S-function as “the function of permeability and porosity for radial-direction which should be used for radial composite model to reproduce the pressure transient behavior of particular outer and inner boundary shapes”. The pressure behavior of radial composite model includes all the type of pressure curves. For example, one can realize any pressure transient behavior (channel type, sealing fault and hydraulic fractured well, etc) with radial model by assigning the permeability and porosity distribution along radial direction adequately. We found that the S-function can be easily estimated from the steady state stream function. The composite models with the S-functions reproduce “sealing fault”, “channel type”, “horizontal sink” and “the reservoir which has different transmissibility regions”. We compared the results with the conventional analytical model by commercial software (Kappa Saphir), and obtained excellent agreement. Not only its high novelty and expandability, but its calculation speed and visibility, this methodology (S-function) will be a powerful tool for pressure transient analysis.