Date of Award

1989

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Petroleum Engineering

First Advisor

Julius P. Langlinais

Abstract

A three-dimensional (3-D) analytical model was developed to improve the analyses of the transient pressure response of a reservoir to wireline formation testing (WFT). Available analysis techniques of the WFT oversimplify the flow geometry by assuming either a radial or a spherical flow pattern. The proposed model simulates the exact flow geometry of the WFT flow pattern. The model was derived by solving the 3-D diffusivity equation coupled with the boundary conditions prevailing during the test. The Laplace transformation and the separation of variables were used to obtain the solution. The solution is expressed in terms of the infinite Fourier-Bessel series in the Laplace space and inverted into the real space by means of Stefhest algorithm. The reduced versions of the 3-D transient model were compared to published 2-D and 1-D models in the literature to verify the solution. Excellent agreement was obtained between the models. The mathematical model was used to evaluate the validity of current interpretation techniques and to investigate the sensitivity of transient pressure behavior to wellbore parameters. A new interpretation technique and a proposed new design for the tool resulted from this study. The study was extended to obtain an analytical model describing laminar flow through a gravel pack in the annular space between a perforation and the gravel screen. An electrical analog was built to verify the mathematical solution. The mathematical solution compared favorably with the experimental data. The analytical model was then used to investigate the effects of several wellbore parameters on the productivity of a gravel packed well. The sensitivity of pressure losses across the pack to perforation size, perforation density, phasing angle, and gravel anisotropy were examined. The perforation size and perforation shot density were identified as the most important parameters.

Pages

149

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