1.0 Introduction
1.1 Problem Statement
Well productivity is one of the major concerns in oil field development, and provides the means for oil field development strategy. Sometimes, well performance is measured in terms of productivity index. In order to arrive at the economic feasibility of drilling a well, petroleum engineers require proven and reliable methods to estimate the expected productivity of that well. Well productivity is often evaluated using the productivity index, defined as the production rate per unit pressure drawdown. Petroleum engineers often relate the well productivity evaluation to the long-time performance behaviour of a well, that is, the behaviour during pseudo-steady-state or/and steady-state flow of a closed system or/and constant pressure system respectively.
The long-term productivity of oil wells is influenced by many factors. Among these factors are petrophysical properties, fluid properties, degree of formation damage and/or stimulation, well geometry, well completions, number of fluid phases, and flow-velocity type (Darcy, non-Darcy) (Yildiz, 2003).
Depending upon the type of wellbore completion configuration, it is possible to have radial, spherical or hemispherical flow near the wellbore. A well with a limited perforated interval (partial completion) could result in spherical flow in the vicinity of the perforations as depicted in fig. 2.1. A well which only partially penetrates the pay zone, could result in hemispherical flow. These conditions could arise where coning of bottom water or gas cap becomes a serious issue (Ahmed, 2005). Figures 3.1 and 3.2 respectively depict the true picture of radial and spherical flow behaviour in a partially completed vertical well.
Partial completion is the completion of or flow from less than the entire producing interval. This situation causes a near-well flow constriction that result in a positive skin effect in a well-test analysis. The net result of partial completion yields extra pressure drop in the near wellbore region and reduces the well productivity.
The present analytical method of evaluating productivity index in vertical wells with partial completion does not account for the effect of pressure drop due to partial completion.
The purpose of this study is to develop analytical model for evaluating productivity index (P.I) of vertical wells with partial completion, where the effect of pressure drop due to partial completion is taken into account and compare results with conventional methods.
The partial differential equations were solved for both no-flow boundary and constant pressure boundary systems in Laplace and Fourier Transform domains before inversion to real time domain.
1.3 Objectives of Study
The main objectives of this work are to:
- Develop analytical model for pressure behaviour in closed and constant pressure boundary systems
- Develop an analytical model for evaluating productivity index of vertical wells with partial completion for both closed-boundary and constant pressure boundary systems taking into account the effect of pressure drop due to partial completion
- Calculate shape factors and compare with the existing ones and
- Investigate the factors and parameters that influence or control productivity index.
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