A new method for analysing productivity index (PI) on vertical wells
is the main objective of this study. Well performance is often measured
in terms of the well’s productivity which is dependent on a number of
factors such as the reservoir’s configuration, the type of completion,
petrophysical and fluid properties, formation damage, etc. The effect of
partial completion is the main focus of making the productivity index
analysis since almost all vertical wells are partially completed due to
the reasons of water coning or gas cap issue, etc. It is also very
expensive to fully complete a well especially when the formation
thickness is so large.
Pressure behaviour solutions for both closed boundary and constant
pressure boundary have been obtained, taking into consideration the
effect of partial completion.
Productivity of a well is usually evaluated on the long time
performance behaviour, thus the pseudo-steady state (late time) approach
has been employed for calculation of the productivity index.
Several key factors have been tested on productivity index such as
pseudo skin, shape factors, penetration ratio, reservoir drainage area
and etc. The effects of these factors have been analysed on PI.
Theoretical data were used in carrying out the analysis with results
indicating that, productivity index increases with increasing completion
interval and vice versa, whiles pressure drop due to skin as a result
of restricted entry to fluid flow increases tremendously with decreasing
Shape factors of various well positions in bounded reservoirs were
computed and compared with results obtained by Dietz, and Babu and Odeh.
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
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
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.
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.