An Approximate Infinite Conductivity Solution for a Partially Penetrating Line-Source Well

Abstract

Abstract A review of previous studies of transient flow to partially penetrating wells was made. All analytical studies involved the assumption of a constant flux along the open interval. This analytical study is a new solution that closely approximates an infinite-conductivity line source (constant pressure along the producing interval). Introduction The problem of fluid flow to wells with partial penetration or restricted entry has received much penetration or restricted entry has received much attention in the last 15 years, both in ground-water hydrologyl and in petroleum engineering. A number of steady-state and unsteady-state solutions have appeared in the literature, and methods for analyzing pressure data have been proposed by several authors. pressure data have been proposed by several authors. Some of these methods have been aimed at determining the reservoir vertical permeability. Although many different techniques have been used for solving the partial penetration problem (namely, the point-source solution, Fourier and Laplace transforms, Hankel and Laplace transforms, Green's functions, finite differences, finite elements, an electric analyzer, a thermal model, and a fluid flow model), the analytical expressions and the numerical results obtained for reservoir pressures by the different methods were essentially identical. There were some differences, however, between the values of wellbore pressures computed from numerical models and those obtained from analytical solutions. Analytical solutions were derived by making the assumption of uniform fluid withdrawal along the portion of the wellbore open to flow. With the nomenclature of Fig. 1, this is written as(1) It appears more realistic to expect the producing pressure to be independent of n Producing pressures pressure to be independent of n Producing pressures would differ only by virtue of the potential head of flowing fluid and friction over the producing interval, assuming the wellbore is open. SPEJ P. 140