New Exact Spherical Flow Solution With Storage for Early-Time Test Interpretation With Applications to Early-Evaluation Drillstem and Wireline Formation Testing

摘要

Conventional methods used to analyze early-time formation transient test data are approzimate and do not model the entire timewise pressure response. Alternatively, detailed models used for early-time storage or late-time analysis are numerical and chart-oriented, and not amenable to simple physical interpretation. In this paper, the general spherical flow formulation, with wellbore storage, is solved by inverting the Laplace transform to produce a closed-from analytical solution. This new solution reduces to previously published early- and late-time solutions in the respective asymptotic limits. Importantly, the availability of the new solution permits convenient pressure-response-to-theory-matching using the complete time regime (early-, transitional-, and late-time data), rather than the rypical late-time matching to the asymptotic limit of the spherical flow regime. The new solution also allows accurate formation evaluation using early- and intermediate-time data only, thereby reducing rig down-time required for testing.