A New Technique for Linear Boundary Detection with Wellbore Storage and Wellbore Skin

This paper presents an analytical solution for a finite radius well with wellbore storage and skin in a two-composite reservoir separated by a linear boundary. The constant-pressure and impermeable linear boundary are limiting forms of the composite case. The solution technique, which employs the Laplace transformation and the addition theorem for Bessel functions, is new and is different from past works. This solution is a subset of a generalized multi-well composite-reservoir solution.¹ 

An analysis technique, both predictive and interpretive, for detecting an impermeable linear boundary using pressure transient data from a well with storage and skin is presented. A new set of pressure and pressure-derivative type curves are advanced along with a new correlating parameter, C_D e^s / L_D. This parameter correlates all the responses when C_D / L_D²  ≥ 0.1, where combined effects of wellbore storage and the boundary interfere with the formation of the first infinite-acting, semi-log straight line. The interpretation technique yields estimates of the distance to the linear boundary, reservoir transmissivity and wellbore storage. The effects of a constant-pressure linear boundary on a constant-rate well with storage and skin are discussed. Also, the parametric behavior of true composite reservoirs separated by a linear boundary is presented.