A composite analytical model for analysis of pumping tests affected by well bore storage and finite thickness skin

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Abstract
A composite analytical model is developed for analyzing the results of pumping tests where the influence of well bore storage and a skin region of finite thickness are present at the pumping well. The solution of the boundary value problem for dimensionless drawdown in the pumping well, skin region, and formation is derived using the Laplace transform method. The solution is verified by comparison to solutions of pumping test problems with well bore storage only, with a composite formation only, and with well bore storage and infinitesimally thin skin. Type curves obtained by numerically inverting the solution for drawdown in the formation are used to illustrate the influence of well bore storage, the effect of skin region characteristics, and the effect of radial distance. These show that the influence of a finite thickness skin of reduced permeability is clearly identifiable over a fairly broad range of radial distance from the pumping well when well bore storage effects are minimized. Conversely, the effects of finite skin of enhanced permeability are more easily identified where the influence of well bore storage is greater. In both cases the type curves are uniquely defined provided that the skin region is of nonzero thickness. Type curves obtained for the solution for drawdown in the skin region are used to illustrate the effect of outer or far‐field boundary conditions. These type curves show that early time data not influenced by well bore storage effects are required to detect the presence of outer boundaries of reduced permeability. Drawdown data at late time, although less influenced by well bore storage effects, are subject to nonuniqueness with regard to the characteristics of the skin and formation regions. Outer boundaries of enhanced permeability are identified only at early time and are almost entirely masked by well bore storage at later time.